Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001246
(load all 4 compositions to match this statistic)
Mapping
St001246: 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] => 1
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 2
[2,1,4,3] => 3
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 2
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 2
[1,2,5,3,4] => 3
[1,2,5,4,3] => 3
[1,3,2,4,5] => 2
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 3
[1,3,5,4,2] => 2
[1,4,2,3,5] => 3
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 3
[1,4,5,3,2] => 3
Description
The maximal difference between two consecutive entries of a permutation. This is given, for a permutation $\pi$ of length $n$, by $$\max\{ | \pi(i) - \pi(i+1) | : 1 \leq i < n \}.$$
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,0,1,0]
 => [1,0,1,0]
 => 1
[2,1] => [1,2] => [1,0,1,0]
 => [1,0,1,0]
 => 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[2,1,3] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[2,3,1] => [1,2,3] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 2
[3,1,2] => [1,2,3] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 2
[3,2,1] => [1,2,3] => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2
[1,3,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 2
[1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[1,4,3,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[2,1,3,4] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 2
[2,1,4,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[2,3,1,4] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[2,3,4,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[2,4,1,3] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 3
[2,4,3,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2
[3,1,2,4] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2
[3,1,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[3,2,1,4] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[3,2,4,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 3
[3,4,1,2] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[3,4,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2
[4,1,2,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[4,1,3,2] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 3
[4,2,1,3] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2
[4,2,3,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2
[4,3,1,2] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2
[4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1
[1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,2,4,5,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ? = 2
[1,2,5,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3
[1,2,5,4,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3
[1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => ? = 3
[1,3,4,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ? = 3
[1,3,4,5,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ? = 3
[1,3,5,2,4] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 3
[1,3,5,4,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 2
[1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3
[1,4,2,5,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 3
[1,4,3,2,5] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 3
[1,4,3,5,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3
[1,4,5,2,3] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 3
[1,4,5,3,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 3
[1,5,2,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,5,2,4,3] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,5,3,2,4] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,5,3,4,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,5,4,2,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,5,4,3,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,1,3,4,5] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ? = 2
[2,1,3,5,4] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 2
[2,1,4,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3
[2,1,4,5,3] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 3
[2,1,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,1,5,4,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,3,1,4,5] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 3
[2,3,1,5,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,3,4,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,3,4,5,1] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[2,3,5,1,4] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 4
[2,3,5,4,1] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 3
[2,4,1,3,5] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 3
[2,4,1,5,3] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,4,3,1,5] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,4,3,5,1] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 4
[3,1,5,2,4] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[3,1,5,4,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[3,2,1,5,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[3,2,4,1,5] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[3,4,1,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[3,4,2,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,1,5,2,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,1,5,3,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,2,1,5,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,2,3,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,3,1,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[4,3,2,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,2,4,5,3] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,2,5,4,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,2,4,5] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,2,5,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,4,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,4,5,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,5,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,3,5,4,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,4,2,3,5] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,4,2,5,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,4,3,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,6,4,3,5,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001879
Mapping
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 80%
Values
[1,2] => [2,1] => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1
[2,1] => [1,2] => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1
[1,2,3] => [2,3,1] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1
[1,3,2] => [3,2,1] => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2
[2,1,3] => [1,3,2] => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 2
[2,3,1] => [1,2,3] => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 2
[3,1,2] => [3,1,2] => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 2
[3,2,1] => [2,1,3] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1
[1,2,3,4] => [2,3,4,1] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[1,2,4,3] => [2,4,3,1] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[1,3,2,4] => [3,2,4,1] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[1,3,4,2] => [4,2,3,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[1,4,2,3] => [3,4,2,1] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[1,4,3,2] => [4,3,2,1] => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,1,3,4] => [1,3,4,2] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[2,1,4,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,3,1,4] => [1,2,4,3] => [.,[.,[[.,.],.]]]
 => ([(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] => [1,4,2,3] => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,4,3,1] => [1,3,2,4] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[3,1,2,4] => [3,1,4,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,1,4,2] => [4,1,3,2] => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[3,2,1,4] => [2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,2,4,1] => [2,1,3,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,4,1,2] => [4,1,2,3] => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[3,4,2,1] => [3,1,2,4] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[4,1,2,3] => [3,4,1,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[4,1,3,2] => [4,3,1,2] => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,2,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[4,2,3,1] => [2,3,1,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[4,3,1,2] => [4,2,1,3] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2
[4,3,2,1] => [3,2,1,4] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[1,2,3,4,5] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1
[1,2,3,5,4] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2
[1,2,4,3,5] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2
[1,2,4,5,3] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2
[1,2,5,3,4] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[1,2,5,4,3] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3
[1,3,2,4,5] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2
[1,3,2,5,4] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[1,3,4,2,5] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[1,3,4,5,2] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,3,5,2,4] => [4,2,5,3,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[1,3,5,4,2] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[1,4,2,3,5] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[1,4,2,5,3] => [3,5,2,4,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[1,4,3,2,5] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3
[1,4,3,5,2] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[1,4,5,2,3] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3
[1,4,5,3,2] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[1,5,2,3,4] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[1,5,2,4,3] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[1,5,3,2,4] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[1,5,3,4,2] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[1,5,4,2,3] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[1,5,4,3,2] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,1,3,4,5] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[2,1,3,5,4] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[2,1,4,3,5] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[2,1,4,5,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[2,1,5,3,4] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4
[2,1,5,4,3] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,3,1,4,5] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[2,3,1,5,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,3,4,1,5] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => ([(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] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,3,5,4,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3
[2,4,1,5,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,4,5,1,3] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,5,1,4,3] => [1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,1,5,4,2] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,4,1,5,2] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,4,5,1,2] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,5,1,4,2] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,1,5,3,2] => [5,4,1,3,2] => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,5,1,3,2] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,4,3,2] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,6,5,4,3,2] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,1,6,5,4,3] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,1,6,5,4] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,1,6,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,5,1,6] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,4,6,1,5] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,5,1,6,4] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,5,6,1,4] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,3,6,1,5,4] => [1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,1,6,5,3] => [1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,5,1,6,3] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,5,6,1,3] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,4,6,1,5,3] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,5,1,6,4,3] => [1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,5,6,1,4,3] => [1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,6,1,5,4,3] => [1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,1,6,5,4,2] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,4,1,6,5,2] => [6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,4,5,1,6,2] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,4,5,6,1,2] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,4,6,1,5,2] => [6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(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
Mapping
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 80%
Values
[1,2] => [2,1] => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1 + 1
[2,1] => [1,2] => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1 + 1
[1,2,3] => [2,3,1] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1 + 1
[1,3,2] => [3,2,1] => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[2,1,3] => [1,3,2] => [.,[[.,.],.]]
 => ([(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] => [3,1,2] => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[3,2,1] => [2,1,3] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 1 + 1
[1,2,3,4] => [2,3,4,1] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[1,2,4,3] => [2,4,3,1] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[1,3,2,4] => [3,2,4,1] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[1,3,4,2] => [4,2,3,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[1,4,2,3] => [3,4,2,1] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[1,4,3,2] => [4,3,2,1] => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,1,3,4] => [1,3,4,2] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[2,1,4,3] => [1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,3,1,4] => [1,2,4,3] => [.,[.,[[.,.],.]]]
 => ([(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] => [1,4,2,3] => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,4,3,1] => [1,3,2,4] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[3,1,2,4] => [3,1,4,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,1,4,2] => [4,1,3,2] => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[3,2,1,4] => [2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,2,4,1] => [2,1,3,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,4,1,2] => [4,1,2,3] => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[3,4,2,1] => [3,1,2,4] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[4,1,2,3] => [3,4,1,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[4,1,3,2] => [4,3,1,2] => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,2,1,3] => [2,4,1,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[4,2,3,1] => [2,3,1,4] => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[4,3,1,2] => [4,2,1,3] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[4,3,2,1] => [3,2,1,4] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[1,2,3,4,5] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 1
[1,2,3,5,4] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,2,4,3,5] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,2,4,5,3] => [2,5,3,4,1] => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,2,5,3,4] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,2,5,4,3] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,3,2,4,5] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,2,5,4] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,3,4,2,5] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,3,4,5,2] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,3,5,2,4] => [4,2,5,3,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,3,5,4,2] => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[1,4,2,3,5] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,4,2,5,3] => [3,5,2,4,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,4,3,2,5] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,3,5,2] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,4,5,2,3] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,5,3,2] => [5,4,2,3,1] => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[1,5,2,3,4] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,5,2,4,3] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,5,3,2,4] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[1,5,3,4,2] => [5,3,4,2,1] => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,5,4,2,3] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[1,5,4,3,2] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,1,3,4,5] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[2,1,3,5,4] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[2,1,4,3,5] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[2,1,4,5,3] => [1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[2,1,5,3,4] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[2,1,5,4,3] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,3,1,4,5] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[2,3,1,5,4] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,3,4,1,5] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => ([(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] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,3,5,4,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[2,4,1,5,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,4,5,1,3] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,5,1,4,3] => [1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,1,5,4,2] => [5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,4,1,5,2] => [5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,4,5,1,2] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,5,1,4,2] => [5,1,4,2,3] => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[4,1,5,3,2] => [5,4,1,3,2] => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[4,5,1,3,2] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,4,3,2] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,6,5,4,3,2] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,1,6,5,4,3] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,1,6,5,4] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,1,6,5] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,5,1,6] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,4,6,1,5] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,5,1,6,4] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,5,6,1,4] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,3,6,1,5,4] => [1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,1,6,5,3] => [1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,5,1,6,3] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,5,6,1,3] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,4,6,1,5,3] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,5,1,6,4,3] => [1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,5,6,1,4,3] => [1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,6,1,5,4,3] => [1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,1,6,5,4,2] => [6,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,4,1,6,5,2] => [6,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,4,5,1,6,2] => [6,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,4,5,6,1,2] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,4,6,1,5,2] => [6,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(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.