Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001247
Mapping
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001247: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,0,1,0,1,0]
 => [2,1]
 => [1]
 => 1
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,0,1,1,0,0]
 => [1,1]
 => [1]
 => 1
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [2,1]
 => 1
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,1,0,0,1,0,1,0]
 => [3,2]
 => [2]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,1]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [1,1,0,1,0,0,1,0]
 => [3,1]
 => [1]
 => 1
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [2,1]
 => 1
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => [2]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,1]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1]
 => 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1]
 => 2
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [1]
 => 1
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,1]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1]
 => 1
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1]
 => 2
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [1,1,0,1,0,1,0,0]
 => [2,1]
 => [1]
 => 1
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,1]
 => [1]
 => 1
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [3,2,1]
 => 2
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [3,2]
 => 1
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [3,1,1]
 => 3
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [3,1]
 => 2
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [3]
 => 1
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [3,1]
 => 2
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [3]
 => 1
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [2,2,1]
 => 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [2,2]
 => 0
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [2,1,1]
 => 2
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [2,1]
 => 1
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [2]
 => 0
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [2,1]
 => 1
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [2]
 => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,1,1]
 => 3
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1]
 => 2
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1]
 => 1
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1]
 => 2
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1]
 => 1
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [2,1,1]
 => 2
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [2,1]
 => 1
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [2]
 => 0
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [2,1]
 => 1
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [2]
 => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,1,1]
 => 3
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1]
 => 2
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1]
 => 1
Description
The number of parts of a partition that are not congruent 2 modulo 3.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 11%
Values
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0],[1,-1,1,0],[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 + 5
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 5
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 5
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 5
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 5
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 5
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,0,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[1,-1,1,-1,0,1],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
[[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5 = 0 + 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.