Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000060
(load all 3 compositions to match this statistic)
Mapping
St000060: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 1
[2,1] => 1
[1,2,3] => 2
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 3
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 3
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 3
[2,3,1,4] => 1
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 3
[4,3,2,1] => 3
[1,2,3,4,5] => 4
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 3
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 2
[1,3,4,5,2] => 4
[1,3,5,2,4] => 3
[1,3,5,4,2] => 4
[1,4,2,3,5] => 3
[1,4,2,5,3] => 3
[1,4,3,2,5] => 2
[1,4,3,5,2] => 3
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
Description
The greater neighbor of the maximum. Han [2] showed that this statistic is (up to a shift) equidistributed on zigzag permutations (permutations $\pi$ such that $\pi(1) < \pi(2) > \pi(3) \cdots$) with the smallest path leaf label of the binary tree associated to a permutation ([[St000724]]), see also [3].
Matching statistic: St001879
(load all 3 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 80%
Values
[1,2] => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1
[2,1] => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1
[1,2,3] => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 2
[1,3,2] => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 2
[2,1,3] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1
[2,3,1] => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 2
[3,1,2] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1
[3,2,1] => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,2,4,3] => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[1,3,4,2] => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,4,2,3] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[2,3,4,1] => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[2,4,3,1] => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,1,4,2] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,2,1,4] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[3,2,4,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,4,2,1] => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,1,2,3] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[4,1,3,2] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[4,2,1,3] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[4,2,3,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[4,3,1,2] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[4,3,2,1] => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,5,4,2,1] => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,5,3,2,1] => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 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.
Matching statistic: St001880
(load all 3 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 80%
Values
[1,2] => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1 + 1
[2,1] => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1 + 1
[1,2,3] => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,3,2] => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[2,1,3] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1 + 1
[2,3,1] => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[3,1,2] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1 + 1
[3,2,1] => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,2,4,3] => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[1,3,4,2] => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,4,2,3] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,3,4,1] => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[2,4,3,1] => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[3,1,2,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,1,4,2] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,2,1,4] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[3,2,4,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,4,2,1] => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,1,2,3] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[4,1,3,2] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[4,2,1,3] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[4,2,3,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[4,3,1,2] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[4,3,2,1] => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 1
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 1
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,5,4,2,1] => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[4,5,3,2,1] => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.