- FindStat

Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000811

Mapping

St000811: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1]
 => 1
[2]
 => 0
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 0
[1,1,1]
 => 4
[4]
 => 0
[3,1]
 => 1
[2,2]
 => 2
[2,1,1]
 => 0
[1,1,1,1]
 => 10
[5]
 => 1
[4,1]
 => 0
[3,2]
 => 0
[3,1,1]
 => 2
[2,2,1]
 => 2
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 26
[6]
 => 0
[5,1]
 => 1
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 4
[3,2,1]
 => 0
[3,1,1,1]
 => 4
[2,2,2]
 => 0
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 76
[7]
 => 1
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 2
[4,3]
 => 0
[4,2,1]
 => 0
[4,1,1,1]
 => 0
[3,3,1]
 => 4
[3,2,2]
 => 2
[3,2,1,1]
 => 0
[3,1,1,1,1]
 => 10
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 8
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 232
[8]
 => 0
[7,1]
 => 1
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 1
[5,2,1]
 => 0

Description

The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. For example,

$p_{22} = s_{1111} - s_{211} + 2s_{22} - s_{31} + s_4$ , so the statistic on the partition

$22$ is 2. This is also the sum of the character values at the given conjugacy class over all irreducible characters of the symmetric group. [2] For a permutation

$\pi$ of given cycle type, this is also the number of permutations whose square equals

$\pi$ . [2]

Matching statistic: St001629

Mapping

Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 7% ●values known / values provided: 37%●distinct values known / distinct values provided: 7%

Values

[1]
 => [1,0]
 => [1] => [1] => ? = 1
[2]
 => [1,0,1,0]
 => [1,1] => [2] => ? ∊ {0,2}
[1,1]
 => [1,1,0,0]
 => [2] => [1] => ? ∊ {0,2}
[3]
 => [1,0,1,0,1,0]
 => [1,1,1] => [3] => 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,2] => [1,1] => ? ∊ {0,4}
[1,1,1]
 => [1,1,0,1,0,0]
 => [3] => [1] => ? ∊ {0,4}
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1] => [4] => 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,2] => [2,1] => 0
[2,2]
 => [1,1,1,0,0,0]
 => [3] => [1] => ? ∊ {0,2,10}
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3] => [1,1] => ? ∊ {0,2,10}
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [4] => [1] => ? ∊ {0,2,10}
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => [5] => 1
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => [3,1] => 0
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,3] => [1,1] => ? ∊ {0,2,2,26}
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => [2,1] => 0
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [4] => [1] => ? ∊ {0,2,2,26}
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,4] => [1,1] => ? ∊ {0,2,2,26}
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5] => [1] => ? ∊ {0,2,2,26}
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1] => [6] => 1
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,2] => [4,1] => 0
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => [2,1] => 0
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,3] => [3,1] => 0
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [4] => [1] => ? ∊ {0,0,4,4,4,76}
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4] => [1,1] => ? ∊ {0,0,4,4,4,76}
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,4] => [2,1] => 0
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [4] => [1] => ? ∊ {0,0,4,4,4,76}
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [5] => [1] => ? ∊ {0,0,4,4,4,76}
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,4,4,4,76}
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,4,4,4,76}
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1] => [7] => 1
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,2] => [5,1] => 0
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,3] => [3,1] => 0
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,3] => [4,1] => 0
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,4] => [1,1] => ? ∊ {0,0,2,2,4,8,10,232}
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,4] => [2,1] => 0
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,4] => [3,1] => 0
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [5] => [1] => ? ∊ {0,0,2,2,4,8,10,232}
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,4] => [1,1] => ? ∊ {0,0,2,2,4,8,10,232}
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,2,2,4,8,10,232}
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,5] => [2,1] => 0
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [5] => [1] => ? ∊ {0,0,2,2,4,8,10,232}
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,2,2,4,8,10,232}
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,6] => [1,1] => ? ∊ {0,0,2,2,4,8,10,232}
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [7] => [1] => ? ∊ {0,0,2,2,4,8,10,232}
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1] => [8] => 1
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,2] => [6,1] => 0
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,3] => [4,1] => 0
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,3] => [5,1] => 0
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,4] => [2,1] => 0
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,4] => [3,1] => 0
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,4] => [4,1] => 0
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [5] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,4] => [2,1] => 0
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,5] => [2,1] => 0
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,5] => [3,1] => 0
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,6] => [1,1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,6] => [2,1] => 0
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [5] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [7] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,7] => [1,1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [8] => [1] => ? ∊ {0,0,1,2,4,4,8,12,20,26,764}
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1] => [9] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,2] => [7,1] => 0
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,3] => [5,1] => 0
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,3] => [6,1] => 0
[6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,4] => [3,1] => 0
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,4] => [4,1] => 0
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,4] => [5,1] => 0
[5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,5] => [2,1] => 0
[5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,4] => [3,1] => 0
[5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,5] => [3,1] => 0
[5,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,5] => [4,1] => 0
[4,4,1]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[4,3,2]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[4,3,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,6] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[4,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,5] => [2,1] => 0
[4,2,1,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,6] => [2,1] => 0
[4,1,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,6] => [3,1] => 0
[3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,3,2,1]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,3,1,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [7] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,2,2,2]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,5] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,2,2,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,6] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,2,1,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,7] => [1,1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[3,1,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,7] => [2,1] => 0
[2,2,2,2,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [6] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[2,2,2,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [7] => [1] => ? ∊ {0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[8,2]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,3] => [6,1] => 0
[8,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,3] => [7,1] => 0
[7,3]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,4] => [4,1] => 0
[7,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,4] => [5,1] => 0
[7,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,4] => [6,1] => 0
[6,4]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,5] => [2,1] => 0
[6,3,1]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,5] => [3,1] => 0

Description

The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.

Matching statistic: St001498
(load all 6 compositions to match this statistic)

Mapping

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 30%●distinct values known / distinct values provided: 3%

Values

[1]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? = 1
[2]
 => [1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {0,2}
[1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {0,2}
[3]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,1,4}
[2,1]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {0,1,4}
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,1,4}
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 0
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {1,2,10}
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {1,2,10}
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {1,2,10}
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 0
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 0
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,1,2,2,26}
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,1,2,2,26}
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,1,2,2,26}
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,1,2,2,26}
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,1,2,2,26}
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 0
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => 0
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 0
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,4,4,4,76}
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 0
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 0
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
 => 0
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => 0
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
 => ? ∊ {0,0,1,2,2,4,8,10,232}
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => 0
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
 => 0
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => 0
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
 => 0
[2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
 => ? ∊ {0,0,1,1,2,4,4,8,12,20,26,764}
[9]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[8,1]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[7,2]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[7,1,1]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0
[6,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => 0
[6,1,1,1]
 => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 0
[5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[5,2,1,1]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 0
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,2,2,4,4,10,10,12,16,52,76,2620}
[4,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0
[3,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => 0
[2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 0
[2,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0
[6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0
[6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => 0
[6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => 0
[6,2,1,1]
 => [1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => 0
[6,1,1,1,1]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0
[5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0
[5,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 0
[4,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => 0
[3,3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => 0
[3,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => 0
[2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0
[2,2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 0
[6,5]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => 0
[6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => 0
[6,3,2]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => 0
[6,3,1,1]
 => [1,1,1,0,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => 0
[6,2,2,1]
 => [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => 0

Description

The normalised height of a Nakayama algebra with magnitude 1. We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.

Matching statistic: St001876

Mapping

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 9%●distinct values known / distinct values provided: 7%

Values

[1]
 => [1,0,1,0]
 => [[1,1],[]]
 => ([],1)
 => ? = 1
[2]
 => [1,1,0,0,1,0]
 => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,2}
[1,1]
 => [1,0,1,1,0,0]
 => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,2}
[3]
 => [1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,1,4}
[2,1]
 => [1,0,1,0,1,0]
 => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,1,4}
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[2,2,1],[]]
 => ([],1)
 => ? ∊ {0,1,4}
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,2,10}
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[3,3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,1,2,2,26}
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[2,2,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [[3,3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [[4,4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [[4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[3,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [[4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [[4,4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [[4,4,4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [[3,3,3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [[3,3,3,3],[2,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [[3,3,3,2],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[2,2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [[3,3,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [[3,3,3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [[4,4,4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [[5,5,5,5,5],[4]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [[5,5,5,5],[4]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [[4,4,4,3],[3]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[4,4,4,4],[3,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[4,4,3],[3]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [[2,2,2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,1,1,1]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [[4,4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,1,1]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[4,4,1,1]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [[4,3,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[3,3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [[4,4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[5,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,3,1,1]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[4,4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0

Description

The number of 2-regular simple modules in the incidence algebra of the lattice.

Matching statistic: St001877

Mapping

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 9%●distinct values known / distinct values provided: 7%

Values

[1]
 => [1,0,1,0]
 => [[1,1],[]]
 => ([],1)
 => ? = 1
[2]
 => [1,1,0,0,1,0]
 => [[2,2],[1]]
 => ([],1)
 => ? ∊ {0,2}
[1,1]
 => [1,0,1,1,0,0]
 => [[2,1],[]]
 => ([],1)
 => ? ∊ {0,2}
[3]
 => [1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,1,4}
[2,1]
 => [1,0,1,0,1,0]
 => [[1,1,1],[]]
 => ([],1)
 => ? ∊ {0,1,4}
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[2,2,1],[]]
 => ([],1)
 => ? ∊ {0,1,4}
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,1,2,10}
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,1,2,10}
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[3,3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,1,2,2,26}
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[2,2,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [[3,3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,1,2,2,26}
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [[4,4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [[4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,1,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[3,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [[4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [[4,4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,1,4,4,4,76}
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [[4,4,4,4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [[3,3,3,3,3],[2]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [[3,3,3,3],[2,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [[3,3,3,2],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3,1],[1]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[2,2,1,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [[3,3,2,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [[3,3,3,3,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [[4,4,4,4,1],[]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,1,2,2,4,8,10,232}
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [[5,5,5,5,5],[4]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [[5,5,5,5],[4]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [[4,4,4,3],[3]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[4,4,4,4],[3,1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[4,4,3],[3]]
 => ([(0,1)],2)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [[2,2,2,2,2],[1]]
 => ([],1)
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,2,4,4,8,12,20,26,764}
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,1,1,1]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [[4,4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,1,1]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[4,4,1,1]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [[4,3,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[3,3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [[4,4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[5,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => ([(0,2),(2,1)],3)
 => 0
[5,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
[4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
[3,3,3,1,1]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[5,3,3,1]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
[5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[4,4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0

Description

Number of indecomposable injective modules with projective dimension 2.