Your data matches 41 different statistics following compositions of up to 3 maps.
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Mp00252: Permutations restrictionPermutations
St000625: Permutations ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2] => 2
[1,3,2] => [1,2] => 2
[2,1,3] => [2,1] => 2
[2,3,1] => [2,1] => 2
[3,1,2] => [1,2] => 2
[3,2,1] => [2,1] => 2
[1,2,3,4] => [1,2,3] => 3
[1,2,4,3] => [1,2,3] => 3
[1,3,2,4] => [1,3,2] => 4
[1,3,4,2] => [1,3,2] => 4
[1,4,2,3] => [1,2,3] => 3
[1,4,3,2] => [1,3,2] => 4
[2,1,3,4] => [2,1,3] => 3
[2,1,4,3] => [2,1,3] => 3
[2,3,1,4] => [2,3,1] => 4
[2,3,4,1] => [2,3,1] => 4
[2,4,1,3] => [2,1,3] => 3
[2,4,3,1] => [2,3,1] => 4
[3,1,2,4] => [3,1,2] => 3
[3,1,4,2] => [3,1,2] => 3
[3,2,1,4] => [3,2,1] => 3
[3,2,4,1] => [3,2,1] => 3
[3,4,1,2] => [3,1,2] => 3
[3,4,2,1] => [3,2,1] => 3
[4,1,2,3] => [1,2,3] => 3
[4,1,3,2] => [1,3,2] => 4
[4,2,1,3] => [2,1,3] => 3
[4,2,3,1] => [2,3,1] => 4
[4,3,1,2] => [3,1,2] => 3
[4,3,2,1] => [3,2,1] => 3
[1,2,3,4,5] => [1,2,3,4] => 4
[1,2,3,5,4] => [1,2,3,4] => 4
[1,2,4,3,5] => [1,2,4,3] => 5
[1,2,4,5,3] => [1,2,4,3] => 5
[1,2,5,3,4] => [1,2,3,4] => 4
[1,2,5,4,3] => [1,2,4,3] => 5
[1,3,2,4,5] => [1,3,2,4] => 5
[1,3,2,5,4] => [1,3,2,4] => 5
[1,3,4,2,5] => [1,3,4,2] => 5
[1,3,4,5,2] => [1,3,4,2] => 5
[1,3,5,2,4] => [1,3,2,4] => 5
[1,3,5,4,2] => [1,3,4,2] => 5
[1,4,2,3,5] => [1,4,2,3] => 5
[1,4,2,5,3] => [1,4,2,3] => 5
[1,4,3,2,5] => [1,4,3,2] => 5
[1,4,3,5,2] => [1,4,3,2] => 5
[1,4,5,2,3] => [1,4,2,3] => 5
[1,4,5,3,2] => [1,4,3,2] => 5
[1,5,2,3,4] => [1,2,3,4] => 4
[1,5,2,4,3] => [1,2,4,3] => 5
Description
The sum of the minimal distances to a greater element. Set $\pi_0 = \pi_{n+1} = n+1$, then this statistic is $$ \sum_{i=1}^n \min_d(\pi_{i-d}>\pi_i\text{ or }\pi_{i+d}>\pi_i) $$ This statistic appears in [1]. The generating function for the sequence of maximal values attained on $\mathfrak S_r$, $r\geq 0$ apparently coincides with [2], which satisfies the functional equation $$ (x-1)^2 (x+1)^3 f(x^2) - (x-1)^2 (x+1) f(x) + x = 0. $$
Mp00223: Permutations runsortPermutations
Mp00072: Permutations binary search tree: left to rightBinary trees
Mp00141: Binary trees pruning number to logarithmic heightDyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% values known / values provided: 9%distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> ? ∊ {2,2,2,2}
[1,3,2] => [1,3,2] => [.,[[.,.],.]]
=> [1,0,1,1,0,0]
=> 2
[2,1,3] => [1,3,2] => [.,[[.,.],.]]
=> [1,0,1,1,0,0]
=> 2
[2,3,1] => [1,2,3] => [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> ? ∊ {2,2,2,2}
[3,1,2] => [1,2,3] => [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> ? ∊ {2,2,2,2}
[3,2,1] => [1,2,3] => [.,[.,[.,.]]]
=> [1,0,1,0,1,0]
=> ? ∊ {2,2,2,2}
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,3,4,2] => [1,3,4,2] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[1,4,3,2] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,1,3,4] => [1,3,4,2] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[2,1,4,3] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,3,1,4] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[2,4,1,3] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[3,1,2,4] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[3,1,4,2] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[3,2,1,4] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> [1,0,1,1,0,0,1,0]
=> 3
[3,2,4,1] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[3,4,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[3,4,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[4,1,2,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[4,1,3,2] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[4,2,1,3] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> [1,0,1,1,1,0,0,0]
=> 3
[4,2,3,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[4,3,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {3,3,3,3,4,4,4,4,4,4,4,4}
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,5,3] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,4,3] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[1,3,4,2,5] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[1,3,4,5,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[1,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[1,3,5,4,2] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[1,4,2,3,5] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,5,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,2,5] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,5,2] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,2,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,3,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,4,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[1,5,3,2,4] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[1,5,3,4,2] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,2,3] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,3,2] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,3,4,5] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[2,1,3,5,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[2,1,4,3,5] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,5,3] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,5,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,5,4,3] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,4,5] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,5,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,1,5] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,5,1,4] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,1,3,5] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[2,4,1,5,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[2,4,3,1,5] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[2,4,3,5,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,5,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[2,4,5,3,1] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,1,3,4] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[2,5,1,4,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,3,1,4] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,4,1,3] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,4,5] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,5,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,5,2,4] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[3,2,4,1,5] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[4,1,3,2,5] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[4,1,3,5,2] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[4,2,1,3,5] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[4,2,5,1,3] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> 5
[4,5,1,3,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[4,5,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,1,3,2,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,1,3,4,2] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,2,1,3,4] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,2,4,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,4,1,3,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[5,4,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [1,0,1,1,1,0,0,0,1,0]
=> 4
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> 7
[1,3,2,5,6,4] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> 7
[1,3,4,2,6,5] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,3,4,6,2,5] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,3,4,6,5,2] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Mp00159: Permutations Demazure product with inversePermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00011: Binary trees to graphGraphs
St000422: Graphs ⟶ ℤResult quality: 9% values known / values provided: 9%distinct values known / distinct values provided: 25%
Values
[1,2,3] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[1,3,2] => [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[2,1,3] => [2,1,3] => [[.,.],[.,.]]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[2,3,1] => [3,2,1] => [[[.,.],.],.]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[3,1,2] => [3,2,1] => [[[.,.],.],.]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[3,2,1] => [3,2,1] => [[[.,.],.],.]
=> ([(0,2),(1,2)],3)
=> ? ∊ {2,2,2,2,2,2}
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,4,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,4,3,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,3,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,3,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,4,1,3] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[2,4,3,1] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,1,2,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,1,4,2] => [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,2,4,1] => [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,4,1,2] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[3,4,2,1] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,1,2,3] => [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,1,3,2] => [4,2,3,1] => [[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,2,1,3] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,2,3,1] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,3,1,2] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4}
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,5,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,4,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,4,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,4,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,5,2,4] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,5,4,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,5,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,2,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,5,2] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,2,3] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,3,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,3,4] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,4,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 6
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,4,6,3,7,5] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,4,7,3,5,6] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,4,7,3,6,5] => [1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,3,5,4,6,7,2] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,3,5,4,7,6,2] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,4,5,2,6,7,3] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,4,5,2,7,6,3] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,4,5,3,6,7,2] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,4,5,3,7,6,2] => [1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
[1,5,3,2,6,7,4] => [1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 8
Description
The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00013: Binary trees to posetPosets
St001879: Posets ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 2
[1,3,2] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 2
[2,1,3] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 2
[2,3,1] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 2
[3,1,2] => [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 2
[3,2,1] => [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,4,2,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,4,1,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[3,1,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[3,1,4,2] => [1,3,4,2] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[3,4,1,2] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[3,4,2,1] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[4,1,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[4,1,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[4,2,1,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[4,2,3,1] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[4,3,1,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4}
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,5,2,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,4,2,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,4,5,2,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,3,2] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,5,2,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,3,2,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,5,3,4,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,2,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,1,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,5,1,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[2,4,1,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,5,1,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,4,5,3,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,1,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,4,1,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,2,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,4,2,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,1,5,4,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,1,2,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,1,5,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,2,1,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,2,5,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,5,1,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,4,5,2,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,1,2,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,1,4,2] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,2,1,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,2,4,1] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,4,1,2] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[3,5,4,2,1] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,2,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,3,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,3,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,5,2,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,1,5,3,2] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,2,1,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00013: Binary trees to posetPosets
St001880: Posets ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[1,3,2] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,1,3] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,3,1] => [1,2,3] => [.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,1,2] => [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,2,1] => [1,3,2] => [.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,4,2,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,4,1,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[3,1,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[3,1,4,2] => [1,3,4,2] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[3,4,1,2] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[3,4,2,1] => [1,3,2,4] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[4,1,2,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[4,1,3,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[4,2,1,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[4,2,3,1] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[4,3,1,2] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ? ∊ {4,4,4,4,4,4,4,4} + 1
[1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,5,2,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,4,2,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,5,3] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,4,5,2,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,3,2] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,3,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,5,2,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,2,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,5,3,4,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,2,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,5,3,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,5,1,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,4,1,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,1,3] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,3,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,4,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,4,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,1,3] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,2,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,4,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,1,2,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,1,5,2] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,2,1,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,2,5,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,5,1,2] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,4,5,2,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,1,2,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,1,4,2] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,2,1,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,2,4,1] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,4,1,2] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,5,4,2,1] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,1,2,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,1,3,2,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,1,3,5,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,1,5,2,3] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,1,5,3,2] => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[4,2,1,3,5] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Mp00252: Permutations restrictionPermutations
Mp00071: Permutations descent compositionInteger compositions
Mp00184: Integer compositions to threshold graphGraphs
St001645: Graphs ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2] => [2] => ([],2)
=> ? ∊ {2,2,2}
[1,3,2] => [1,2] => [2] => ([],2)
=> ? ∊ {2,2,2}
[2,1,3] => [2,1] => [1,1] => ([(0,1)],2)
=> 2
[2,3,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 2
[3,1,2] => [1,2] => [2] => ([],2)
=> ? ∊ {2,2,2}
[3,2,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 2
[1,2,3,4] => [1,2,3] => [3] => ([],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[1,2,4,3] => [1,2,3] => [3] => ([],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[1,3,2,4] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[1,3,4,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[1,4,2,3] => [1,2,3] => [3] => ([],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[1,4,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[2,1,3,4] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[2,1,4,3] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[2,3,1,4] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[2,3,4,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[2,4,1,3] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[2,4,3,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[3,1,2,4] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[3,1,4,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[3,2,1,4] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,2,4,1] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[3,4,1,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[3,4,2,1] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[4,1,2,3] => [1,2,3] => [3] => ([],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[4,1,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[4,2,1,3] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[4,2,3,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 4
[4,3,1,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {3,3,3,3,3,3,3,3,3,3,3,3}
[4,3,2,1] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[1,2,3,4,5] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,3,5,4] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,3,5] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,4,5,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,3,4] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,2,5,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,4,5] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,2,5,4] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,4,2,5] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,4,5,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,5,2,4] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,3,5,4,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,3,5] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,2,5,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,2,5] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,3,5,2] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,2,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,4,5,3,2] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,3,4] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,2,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,3,2,4] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,3,4,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,2,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[1,5,4,3,2] => [1,4,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,3,4,5] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,3,5,4] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,3,5] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,4,5,3] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,5,3,4] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,1,5,4,3] => [2,1,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,4,5] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,1,5,4] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,1,5] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,4,5,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[2,3,5,1,4] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}
[4,3,2,1,5] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,2,5,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,5,2,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,5,3,2,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[5,4,3,2,1] => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[1,5,4,3,2,6] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[1,5,4,3,6,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[1,5,4,6,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[1,5,6,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[1,6,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,5,4,3,1,6] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,5,4,3,6,1] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,5,4,6,3,1] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,5,6,4,3,1] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[2,6,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,5,4,2,1,6] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,5,4,2,6,1] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,5,4,6,2,1] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,5,6,4,2,1] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[3,6,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,5,3,2,1,6] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,5,3,2,6,1] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,5,3,6,2,1] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,5,6,3,2,1] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[4,6,5,3,2,1] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,4,3,2,1,6] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,4,3,2,6,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,4,3,6,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,4,6,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[5,6,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6,1,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6,2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6,3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6,4,5,3,2,1] => [4,5,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
Description
The pebbling number of a connected graph.
Mp00159: Permutations Demazure product with inversePermutations
Mp00208: Permutations lattice of intervalsLattices
Mp00191: Lattices dualLattices
St001845: Lattices ⟶ ℤResult quality: 3% values known / values provided: 3%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> 1 = 2 - 1
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 1 = 2 - 1
[2,1,3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 1 = 2 - 1
[2,3,1] => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> 1 = 2 - 1
[3,1,2] => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> 1 = 2 - 1
[3,2,1] => [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> 1 = 2 - 1
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,3),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)
=> 2 = 3 - 1
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[1,4,2,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[1,4,3,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[2,1,3,4] => [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,3),(4,7),(5,6),(5,7),(6,1),(6,2),(7,8)],9)
=> 2 = 3 - 1
[2,1,4,3] => [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2)],8)
=> 3 = 4 - 1
[2,3,1,4] => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[2,3,4,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[2,4,1,3] => [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2)],8)
=> 3 = 4 - 1
[2,4,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[3,1,2,4] => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[3,1,4,2] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[3,2,1,4] => [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,3),(0,6),(1,8),(2,8),(3,8),(4,2),(4,7),(5,1),(5,7),(6,4),(6,5),(7,8)],9)
=> 2 = 3 - 1
[3,2,4,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[3,4,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[4,1,2,3] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[4,1,3,2] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,2),(5,7),(6,1),(6,7),(7,3),(7,4)],9)
=> 2 = 3 - 1
[4,2,1,3] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[4,2,3,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[4,3,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {3,3,4,4,4,4,4,4} - 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,7),(0,8),(1,15),(2,15),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(10,15),(11,15),(12,10),(12,14),(13,11),(13,14),(14,15)],16)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,2,3,5,4] => [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,6),(0,7),(1,12),(2,12),(3,12),(4,8),(4,10),(5,1),(5,11),(6,4),(6,9),(7,5),(7,9),(8,2),(8,3),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,2,4,3,5] => [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,3),(5,10),(6,4),(6,11),(7,5),(7,9),(8,6),(8,9),(9,10),(9,11),(10,12),(11,1),(11,2)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,2,4,5,3] => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,6),(0,7),(1,11),(2,11),(3,11),(4,2),(4,9),(5,1),(5,9),(6,8),(6,10),(7,3),(7,10),(8,4),(8,5),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,2,5,3,4] => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,6),(0,7),(1,11),(2,11),(3,11),(4,2),(4,9),(5,1),(5,9),(6,8),(6,10),(7,3),(7,10),(8,4),(8,5),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,2,5,4,3] => [1,2,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,6),(0,7),(1,11),(2,11),(3,11),(4,2),(4,9),(5,1),(5,9),(6,8),(6,10),(7,3),(7,10),(8,4),(8,5),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,2,4,5] => [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,3),(5,10),(6,4),(6,11),(7,5),(7,9),(8,6),(8,9),(9,10),(9,11),(10,12),(11,1),(11,2)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,6),(0,7),(1,10),(2,10),(3,10),(4,10),(5,10),(6,3),(6,9),(7,8),(7,9),(8,1),(8,2),(9,4),(9,5)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,4,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,4),(5,10),(6,3),(6,10),(7,2),(7,9),(8,1),(8,9),(9,5),(9,6),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,4,5,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,5,2,4] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,5),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,3),(6,4),(7,1),(7,2),(8,6),(8,7)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,3,5,4,2] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,2,3,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,4),(5,10),(6,3),(6,10),(7,2),(7,9),(8,1),(8,9),(9,5),(9,6),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,2,5,3] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,4),(5,10),(6,3),(6,10),(7,2),(7,9),(8,1),(8,9),(9,5),(9,6),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,3,5,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,5,2,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,4,5,3,2] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,2,3,4] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,2,4,3] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,3,2,4] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,3,4,2] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,4,2,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[1,5,4,3,2] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,3,4,5] => [2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,6),(0,7),(1,12),(2,12),(3,12),(4,8),(4,10),(5,1),(5,11),(6,4),(6,9),(7,5),(7,9),(8,2),(8,3),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,3,5,4] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(5,9),(6,7),(6,9),(7,1),(7,2),(8,3),(8,4),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,4,3,5] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,6),(0,7),(1,10),(2,10),(3,10),(4,10),(5,10),(6,3),(6,9),(7,8),(7,9),(8,1),(8,2),(9,4),(9,5)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,4,5,3] => [2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,4),(5,9),(6,3),(6,9),(7,1),(7,2),(8,5),(8,6),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,5,3,4] => [2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,4),(5,9),(6,3),(6,9),(7,1),(7,2),(8,5),(8,6),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,4),(5,9),(6,3),(6,9),(7,1),(7,2),(8,5),(8,6),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,3,1,4,5] => [3,2,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,6),(0,7),(1,11),(2,11),(3,11),(4,2),(4,9),(5,1),(5,9),(6,8),(6,10),(7,3),(7,10),(8,4),(8,5),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,3,1,5,4] => [3,2,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([(0,7),(0,8),(1,10),(2,10),(3,10),(4,10),(5,4),(5,9),(6,3),(6,9),(7,1),(7,2),(8,5),(8,6),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,3,4,1,5] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,5),(0,8),(1,10),(2,10),(3,10),(4,10),(5,10),(6,2),(6,9),(7,1),(7,9),(8,6),(8,7),(9,3),(9,4)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,3,4,5,1] => [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,7),(0,8),(1,11),(2,11),(3,11),(4,11),(5,4),(5,10),(6,3),(6,10),(7,2),(7,9),(8,1),(8,9),(9,5),(9,6),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[2,3,5,4,1] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,6),(0,7),(1,10),(2,10),(3,10),(4,10),(5,10),(6,4),(6,9),(7,3),(7,9),(8,1),(8,2),(9,5),(9,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,4,1,3,5] => [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,5),(0,8),(1,9),(2,9),(3,9),(4,9),(5,9),(6,3),(6,4),(7,1),(7,2),(8,6),(8,7)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[2,4,3,1,5] => [4,3,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,3),(0,8),(1,12),(2,12),(3,12),(4,6),(4,9),(5,7),(5,9),(6,2),(6,10),(7,1),(7,11),(8,4),(8,5),(9,10),(9,11),(10,12),(11,12)],13)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,4,3,5,1] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,6),(0,7),(1,10),(2,10),(3,10),(4,10),(5,10),(6,4),(6,9),(7,3),(7,9),(8,1),(8,2),(9,5),(9,8)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,4,5,1,3] => [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(5,9),(6,7),(6,9),(7,1),(7,2),(8,3),(8,4),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,4,5,3,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,7),(0,8),(1,15),(2,15),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(10,15),(11,15),(12,10),(12,14),(13,11),(13,14),(14,15)],16)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[2,5,1,4,3] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[2,5,3,1,4] => [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(5,9),(6,7),(6,9),(7,1),(7,2),(8,3),(8,4),(9,10)],11)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[2,5,3,4,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,7),(0,8),(1,15),(2,15),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(10,15),(11,15),(12,10),(12,14),(13,11),(13,14),(14,15)],16)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} - 1
[3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[3,2,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 3 = 4 - 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[1,3,5,2,6,4] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[1,3,6,2,4,5] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[1,3,6,2,5,4] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[1,4,2,6,3,5] => [1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[1,4,3,6,2,5] => [1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[2,3,4,6,1,5] => [5,2,3,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)
=> 4 = 5 - 1
[2,3,5,1,4,6] => [4,2,5,1,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[2,3,5,1,6,4] => [4,2,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,3,5,6,1,4] => [5,2,6,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,3,6,1,4,5] => [4,2,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,3,6,1,5,4] => [4,2,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,3,6,4,1,5] => [5,2,6,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,3,6,5,1,4] => [5,2,6,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,4,1,5,3,6] => [3,5,1,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[2,4,1,5,6,3] => [3,6,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)
=> 4 = 5 - 1
[2,4,1,6,3,5] => [3,5,1,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,4,1,6,5,3] => [3,6,1,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)
=> 4 = 5 - 1
[2,4,3,6,1,5] => [5,3,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)
=> 4 = 5 - 1
[2,4,5,1,6,3] => [4,6,3,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 4 = 5 - 1
[2,5,1,3,4,6] => [3,5,1,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> ([(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2),(7,3),(7,4),(7,5)],9)
=> 4 = 5 - 1
[2,5,1,3,6,4] => [3,6,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,1),(7,2)],9)
=> 4 = 5 - 1
Description
The number of join irreducibles minus the rank of a lattice. A lattice is join-extremal, if this statistic is $0$.
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00209: Permutations pattern posetPosets
Mp00125: Posets dual posetPosets
St000528: Posets ⟶ ℤResult quality: 2% values known / values provided: 2%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[1,3,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,1,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,2,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,2,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,4,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,4,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[1,4,3,2] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,1,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,4,1,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[3,1,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[3,2,1,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[3,4,1,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[3,4,2,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[4,1,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[4,2,1,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[4,3,1,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[4,3,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,4,4,4,4,4,4,4,4} + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,2),(0,4),(1,11),(2,5),(2,6),(2,7),(3,1),(3,8),(3,9),(3,10),(4,3),(4,5),(4,6),(4,7),(5,9),(5,10),(6,8),(6,10),(7,8),(7,9),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,3),(0,4),(1,8),(1,10),(2,7),(2,9),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,4,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,2),(0,3),(1,4),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(3,1),(3,5),(3,6),(3,7),(3,8),(4,13),(5,11),(5,12),(6,10),(6,12),(7,9),(7,12),(8,4),(8,9),(8,10),(8,11),(8,12),(9,13),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
Description
The height of a poset. This equals the rank of the poset [[St000080]] plus one.
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00209: Permutations pattern posetPosets
Mp00125: Posets dual posetPosets
St000912: Posets ⟶ ℤResult quality: 2% values known / values provided: 2%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[1,3,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,1,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,2,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,2,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,4,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,4,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[1,4,3,2] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,1,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,4,1,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,1,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,2,1,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,4,1,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,4,2,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,1,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,2,1,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,3,1,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,3,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,2),(0,4),(1,11),(2,5),(2,6),(2,7),(3,1),(3,8),(3,9),(3,10),(4,3),(4,5),(4,6),(4,7),(5,9),(5,10),(6,8),(6,10),(7,8),(7,9),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,3),(0,4),(1,8),(1,10),(2,7),(2,9),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,4,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,2),(0,3),(1,4),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(3,1),(3,5),(3,6),(3,7),(3,8),(4,13),(5,11),(5,12),(6,10),(6,12),(7,9),(7,12),(8,4),(8,9),(8,10),(8,11),(8,12),(9,13),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
Description
The number of maximal antichains in a poset.
Mp00090: Permutations cycle-as-one-line notationPermutations
Mp00209: Permutations pattern posetPosets
Mp00125: Posets dual posetPosets
St001343: Posets ⟶ ℤResult quality: 2% values known / values provided: 2%distinct values known / distinct values provided: 62%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[1,3,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,1,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,2,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,2,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,3,4,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[1,4,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[1,4,3,2] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,1,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[2,4,1,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,1,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,2,1,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,2,4,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,4,1,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[3,4,2,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,1,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[4,1,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,2,1,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 4 + 1
[4,2,3,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,3,1,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[4,3,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)
=> ? ∊ {3,3,3,3,3,3,3,3,4,4} + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,2,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,2,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,2,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,2,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,4,5,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[1,3,5,2,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,3,5,4,2] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,2,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,2,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,3,5,2] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,2,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,4,5,3,2] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,2,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,2,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,3,4,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,2,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,5,4,3,2] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,1,5,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,1,5,4,3] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,1,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,1,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[2,3,5,1,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,1,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,1,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,3,5,1] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,1,3] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,4,5,3,1] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,1,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,1,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,3,4,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,1,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[2,5,4,3,1] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,2,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ([(0,2),(0,4),(1,11),(2,5),(2,6),(2,7),(3,1),(3,8),(3,9),(3,10),(4,3),(4,5),(4,6),(4,7),(5,9),(5,10),(6,8),(6,10),(7,8),(7,9),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ([(0,3),(0,4),(1,8),(1,10),(2,7),(2,9),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,1,5,4,2] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ([(0,2),(0,3),(1,4),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(3,1),(3,5),(3,6),(3,7),(3,8),(4,13),(5,11),(5,12),(6,10),(6,12),(7,9),(7,12),(8,4),(8,9),(8,10),(8,11),(8,12),(9,13),(10,13),(11,13),(12,13)],14)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[3,2,1,5,4] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ([(0,2),(0,4),(1,8),(2,5),(2,6),(3,1),(3,7),(3,9),(4,3),(4,5),(4,6),(5,9),(6,7),(6,9),(7,8),(9,8)],10)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} + 1
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,3,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,3,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,3,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,2,4,5,6,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,4,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,4,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,2,5,6,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
[1,3,4,2,6,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
Description
The dimension of the reduced incidence algebra of a poset. The reduced incidence algebra of a poset is the subalgebra of the incidence algebra consisting of the elements which assign the same value to any two intervals that are isomorphic to each other as posets. Thus, this statistic returns the number of non-isomorphic intervals of the poset.
The following 31 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000264The girth of a graph, which is not a tree. St001626The number of maximal proper sublattices of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St000080The rank of the poset. St000680The Grundy value for Hackendot on posets. St000906The length of the shortest maximal chain in a poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001782The order of rowmotion on the set of order ideals of a poset. St000245The number of ascents of a permutation. St000703The number of deficiencies of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000097The order of the largest clique of the graph. St001720The minimal length of a chain of small intervals in a lattice. St001581The achromatic number of a graph. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001621The number of atoms of a lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000550The number of modular elements of a lattice. St000553The number of blocks of a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000072The number of circled entries. St000822The Hadwiger number of the graph. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000741The Colin de Verdière graph invariant.