Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001259
(load all 4 compositions to match this statistic)
Mapping
St001259: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 2
[1,0,1,0]
 => 4
[1,1,0,0]
 => 3
[1,0,1,0,1,0]
 => 6
[1,0,1,1,0,0]
 => 5
[1,1,0,0,1,0]
 => 7
[1,1,0,1,0,0]
 => 6
[1,1,1,0,0,0]
 => 4
[1,0,1,0,1,0,1,0]
 => 8
[1,0,1,0,1,1,0,0]
 => 7
[1,0,1,1,0,0,1,0]
 => 9
[1,0,1,1,0,1,0,0]
 => 8
[1,0,1,1,1,0,0,0]
 => 6
[1,1,0,0,1,0,1,0]
 => 8
[1,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,0,1,0]
 => 10
[1,1,0,1,0,1,0,0]
 => 9
[1,1,0,1,1,0,0,0]
 => 7
[1,1,1,0,0,0,1,0]
 => 10
[1,1,1,0,0,1,0,0]
 => 10
[1,1,1,0,1,0,0,0]
 => 8
[1,1,1,1,0,0,0,0]
 => 5
[1,0,1,0,1,0,1,0,1,0]
 => 10
[1,0,1,0,1,0,1,1,0,0]
 => 9
[1,0,1,0,1,1,0,0,1,0]
 => 11
[1,0,1,0,1,1,0,1,0,0]
 => 10
[1,0,1,0,1,1,1,0,0,0]
 => 8
[1,0,1,1,0,0,1,0,1,0]
 => 10
[1,0,1,1,0,0,1,1,0,0]
 => 10
[1,0,1,1,0,1,0,0,1,0]
 => 12
[1,0,1,1,0,1,0,1,0,0]
 => 11
[1,0,1,1,0,1,1,0,0,0]
 => 9
[1,0,1,1,1,0,0,0,1,0]
 => 12
[1,0,1,1,1,0,0,1,0,0]
 => 12
[1,0,1,1,1,0,1,0,0,0]
 => 10
[1,0,1,1,1,1,0,0,0,0]
 => 7
[1,1,0,0,1,0,1,0,1,0]
 => 10
[1,1,0,0,1,0,1,1,0,0]
 => 9
[1,1,0,0,1,1,0,0,1,0]
 => 12
[1,1,0,0,1,1,0,1,0,0]
 => 10
[1,1,0,0,1,1,1,0,0,0]
 => 9
[1,1,0,1,0,0,1,0,1,0]
 => 11
[1,1,0,1,0,0,1,1,0,0]
 => 11
[1,1,0,1,0,1,0,0,1,0]
 => 13
[1,1,0,1,0,1,0,1,0,0]
 => 12
[1,1,0,1,0,1,1,0,0,0]
 => 10
[1,1,0,1,1,0,0,0,1,0]
 => 13
[1,1,0,1,1,0,0,1,0,0]
 => 13
[1,1,0,1,1,0,1,0,0,0]
 => 11
[1,1,0,1,1,1,0,0,0,0]
 => 8
Description
The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 67%
Values
[1,0]
 => [1,1,0,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1 = 2 - 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2 = 3 - 1
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 4 - 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => 4 = 5 - 1
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {6,6,7} - 1
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 4 - 1
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {6,6,7} - 1
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? ∊ {6,6,7} - 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5 = 6 - 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6 = 7 - 1
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 5 - 1
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 6 = 7 - 1
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {8,8,8,8,8,9,9,10,10,10} - 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => 6 = 7 - 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7 = 8 - 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 8 = 9 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 8 = 9 - 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 6 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 9 = 10 - 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {8,9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14} - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
 => 7 = 8 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,1,0,0]
 => 8 = 9 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => 10 = 11 - 1
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => 11 = 12 - 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => 9 = 10 - 1
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9 = 10 - 1
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => 10 = 11 - 1
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 7 - 1
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,1,1,0,0,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => 12 = 13 - 1
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => 11 = 12 - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => 12 = 13 - 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => 10 = 11 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.