Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000933
Mapping
St000933: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 2
[1,1]
 => 1
[3]
 => 3
[2,1]
 => 2
[1,1,1]
 => 1
[4]
 => 5
[3,1]
 => 3
[2,2]
 => 4
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 7
[4,1]
 => 5
[3,2]
 => 6
[3,1,1]
 => 3
[2,2,1]
 => 4
[2,1,1,1]
 => 2
[1,1,1,1,1]
 => 1
[6]
 => 11
[5,1]
 => 7
[4,2]
 => 10
[4,1,1]
 => 5
[3,3]
 => 9
[3,2,1]
 => 6
[3,1,1,1]
 => 3
[2,2,2]
 => 8
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 2
[1,1,1,1,1,1]
 => 1
[7]
 => 15
[6,1]
 => 11
[5,2]
 => 14
[5,1,1]
 => 7
[4,3]
 => 15
[4,2,1]
 => 10
[4,1,1,1]
 => 5
[3,3,1]
 => 9
[3,2,2]
 => 12
[3,2,1,1]
 => 6
[3,1,1,1,1]
 => 3
[2,2,2,1]
 => 8
[2,2,1,1,1]
 => 4
[2,1,1,1,1,1]
 => 2
[1,1,1,1,1,1,1]
 => 1
[8]
 => 22
[7,1]
 => 15
[6,2]
 => 22
[6,1,1]
 => 11
[5,3]
 => 21
[5,2,1]
 => 14
[5,1,1,1]
 => 7
Description
The number of multipartitions of sizes given by an integer partition. This is, for $\lambda = (\lambda_1,\ldots,\lambda_n)$, this is the number of $n$-tuples $(\lambda^{(1)},\ldots,\lambda^{(n)})$ of partitions $\lambda^{(i)}$ such that $\lambda^{(i)} \vdash \lambda_i$.
Matching statistic: St001232
(load all 33 compositions to match this statistic)
Mapping
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 19%
Values
[2]
 => [1,0,1,0]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0 = 1 - 1
[1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1 = 2 - 1
[3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1 = 2 - 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 3 - 1
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 2 - 1
[2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2 = 3 - 1
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {4,5} - 1
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? ∊ {4,5} - 1
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 1 - 1
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 2 - 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2 = 3 - 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {5,6,7} - 1
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3 = 4 - 1
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {5,6,7} - 1
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {5,6,7} - 1
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 1 - 1
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1 = 2 - 1
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2 = 3 - 1
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,0,0]
 => 4 = 5 - 1
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3 = 4 - 1
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {6,7,8,9,10,11} - 1
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 1 - 1
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1 = 2 - 1
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 4 = 5 - 1
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 3 = 4 - 1
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5 = 6 - 1
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {7,8,9,10,11,12,14,15,15} - 1
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 4 = 5 - 1
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => 3 = 4 - 1
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6 = 7 - 1
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5 = 6 - 1
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => 4 = 5 - 1
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => 6 = 7 - 1
[5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5 = 6 - 1
[5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[4,4,1]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => 7 = 8 - 1
[4,3,2]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[4,3,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[4,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => ? ∊ {1,2,3,4,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,4]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => 6 = 7 - 1
[5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 8 = 9 - 1
[5,4,1]
 => [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => 7 = 8 - 1
[6,5]
 => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => 8 = 9 - 1
[5,5,1]
 => [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => 9 = 10 - 1
[6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => 10 = 11 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000454
Mapping
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 12%
Values
[2]
 => [[1,2]]
 => [2] => ([],2)
 => 0 = 1 - 1
[1,1]
 => [[1],[2]]
 => [1,1] => ([(0,1)],2)
 => 1 = 2 - 1
[3]
 => [[1,2,3]]
 => [3] => ([],3)
 => 0 = 1 - 1
[2,1]
 => [[1,3],[2]]
 => [1,2] => ([(1,2)],3)
 => 1 = 2 - 1
[1,1,1]
 => [[1],[2],[3]]
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
[4]
 => [[1,2,3,4]]
 => [4] => ([],4)
 => 0 = 1 - 1
[3,1]
 => [[1,3,4],[2]]
 => [1,3] => ([(2,3)],4)
 => 1 = 2 - 1
[2,2]
 => [[1,2],[3,4]]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 5 - 1
[2,1,1]
 => [[1,4],[2],[3]]
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
[5]
 => [[1,2,3,4,5]]
 => [5] => ([],5)
 => 0 = 1 - 1
[4,1]
 => [[1,3,4,5],[2]]
 => [1,4] => ([(3,4)],5)
 => 1 = 2 - 1
[3,2]
 => [[1,2,5],[3,4]]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {6,7} - 1
[3,1,1]
 => [[1,4,5],[2],[3]]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
[2,2,1]
 => [[1,3],[2,5],[4]]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {6,7} - 1
[2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [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)
 => 4 = 5 - 1
[6]
 => [[1,2,3,4,5,6]]
 => [6] => ([],6)
 => 0 = 1 - 1
[5,1]
 => [[1,3,4,5,6],[2]]
 => [1,5] => ([(4,5)],6)
 => 1 = 2 - 1
[4,2]
 => [[1,2,5,6],[3,4]]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? ∊ {7,8,9,10,11} - 1
[4,1,1]
 => [[1,4,5,6],[2],[3]]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
[3,3]
 => [[1,2,3],[4,5,6]]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? ∊ {7,8,9,10,11} - 1
[3,2,1]
 => [[1,3,6],[2,5],[4]]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {7,8,9,10,11} - 1
[3,1,1,1]
 => [[1,5,6],[2],[3],[4]]
 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
[2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {7,8,9,10,11} - 1
[2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {7,8,9,10,11} - 1
[2,1,1,1,1]
 => [[1,6],[2],[3],[4],[5]]
 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 5 - 1
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5 = 6 - 1
[7]
 => [[1,2,3,4,5,6,7]]
 => [7] => ([],7)
 => 0 = 1 - 1
[6,1]
 => [[1,3,4,5,6,7],[2]]
 => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
[5,2]
 => [[1,2,5,6,7],[3,4]]
 => [2,5] => ([(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[5,1,1]
 => [[1,4,5,6,7],[2],[3]]
 => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
 => 2 = 3 - 1
[4,3]
 => [[1,2,3,7],[4,5,6]]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[4,2,1]
 => [[1,3,6,7],[2,5],[4]]
 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[4,1,1,1]
 => [[1,5,6,7],[2],[3],[4]]
 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 4 - 1
[3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[3,2,1,1]
 => [[1,4,7],[2,6],[3],[5]]
 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[3,1,1,1,1]
 => [[1,6,7],[2],[3],[4],[5]]
 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 4 = 5 - 1
[2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? ∊ {8,9,10,11,12,14,15,15} - 1
[2,1,1,1,1,1]
 => [[1,7],[2],[3],[4],[5],[6]]
 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 5 = 6 - 1
[1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 6 = 7 - 1
[8]
 => [[1,2,3,4,5,6,7,8]]
 => [8] => ([],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[7,1]
 => [[1,3,4,5,6,7,8],[2]]
 => [1,7] => ([(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => [2,6] => ([(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[6,1,1]
 => [[1,4,5,6,7,8],[2],[3]]
 => [1,1,6] => ([(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[5,3]
 => [[1,2,3,7,8],[4,5,6]]
 => [3,5] => ([(4,7),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[5,2,1]
 => [[1,3,6,7,8],[2,5],[4]]
 => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[5,1,1,1]
 => [[1,5,6,7,8],[2],[3],[4]]
 => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,3,1]
 => [[1,3,4,8],[2,6,7],[5]]
 => [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,2,1,1]
 => [[1,4,7,8],[2,6],[3],[5]]
 => [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[4,1,1,1,1]
 => [[1,6,7,8],[2],[3],[4],[5]]
 => [1,1,1,1,4] => ([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,3,1,1]
 => [[1,4,5],[2,7,8],[3],[6]]
 => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,2,2,1]
 => [[1,3,8],[2,5],[4,7],[6]]
 => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,2,1,1,1]
 => [[1,5,8],[2,7],[3],[4],[6]]
 => [1,1,1,2,3] => ([(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[3,1,1,1,1,1]
 => [[1,7,8],[2],[3],[4],[5],[6]]
 => [1,1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,2,1,1]
 => [[1,4],[2,6],[3,8],[5],[7]]
 => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,2,1,1,1,1]
 => [[1,6],[2,8],[3],[4],[5],[7]]
 => [1,1,1,1,2,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[2,1,1,1,1,1,1]
 => [[1,8],[2],[3],[4],[5],[6],[7]]
 => [1,1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[1,1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,25} - 1
[9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [9] => ([],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => [1,8] => ([(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[7,2]
 => [[1,2,5,6,7,8,9],[3,4]]
 => [2,7] => ([(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[7,1,1]
 => [[1,4,5,6,7,8,9],[2],[3]]
 => [1,1,7] => ([(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,3]
 => [[1,2,3,7,8,9],[4,5,6]]
 => [3,6] => ([(5,8),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,2,1]
 => [[1,3,6,7,8,9],[2,5],[4]]
 => [1,2,6] => ([(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[6,1,1,1]
 => [[1,5,6,7,8,9],[2],[3],[4]]
 => [1,1,1,6] => ([(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => [4,5] => ([(4,8),(5,8),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,3,1]
 => [[1,3,4,8,9],[2,6,7],[5]]
 => [1,3,5] => ([(4,8),(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,2,2]
 => [[1,2,7,8,9],[3,4],[5,6]]
 => [2,2,5] => ([(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,2,1,1]
 => [[1,4,7,8,9],[2,6],[3],[5]]
 => [1,1,2,5] => ([(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
[5,1,1,1,1]
 => [[1,6,7,8,9],[2],[3],[4],[5]]
 => [1,1,1,1,5] => ([(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
 => ? ∊ {1,2,3,4,5,6,7,8,9,10,11,12,14,15,15,16,18,20,21,22,22,24,25,27,28,30,30,30,33,35} - 1
Description
The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.