Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000065
(load all 8 compositions to match this statistic)
Mapping
St000065: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 0
[[1,0],[0,1]]
 => 0
[[0,1],[1,0]]
 => 0
[[1,0,0],[0,1,0],[0,0,1]]
 => 0
[[0,1,0],[1,0,0],[0,0,1]]
 => 0
[[1,0,0],[0,0,1],[0,1,0]]
 => 0
[[0,1,0],[1,-1,1],[0,1,0]]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => 0
[[0,1,0],[0,0,1],[1,0,0]]
 => 0
[[0,0,1],[0,1,0],[1,0,0]]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => 0
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => 0
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => 1
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => 1
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => 1
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => 1
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => 0
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => 0
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => 1
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => 0
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => 1
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => 1
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => 0
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => 2
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => 0
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => 0
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => 0
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => 0
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => 0
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => 1
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => 0
Description
The number of entries equal to -1 in an alternating sign matrix. The number of nonzero entries, [[St000890]] is twice this number plus the dimension of the matrix.
Matching statistic: St001431
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001431: Dyck paths ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 20%
Values
[[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => 0
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,3],[3,3],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,2],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,2],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,2],[2,2,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,2],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,1],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,3],[2,3,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,3],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,4],[2,3,4],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,2],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,2],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [5,3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 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]]
 => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
 => [5,4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,1,0,0]
 => ? = 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]
 => [5,4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,1,0,0]
 => ? = 1
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]
 => [5,3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 2
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]
 => [4,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 3
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]]
 => [4,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 2
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,5],[5]]
 => ?
 => ?
 => ? = 2
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]
 => [4,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 2
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,5],[5]]
 => [5,3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 1
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]]
 => [4,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,5],[5]]
 => [4,3,3,3,2]
 => [1,1,0,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 2
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,5],[5]]
 => [4,4,3,2,2]
 => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 1
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,5],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,5],[5]]
 => ?
 => ?
 => ? = 2
Description
Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. The modified algebra B is obtained from the stable Auslander algebra kQ/I by deleting all relations which contain walks of length at least three (conjectural this step of deletion is not necessary as the stable higher Auslander algebras might be quadratic) and taking as B then the algebra kQ^(op)/J when J is the quadratic perp of the ideal I. See http://www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.
Matching statistic: St000074
(load all 4 compositions to match this statistic)
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000074: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 30%
Values
[[1]]
 => [[1]]
 => [[1]]
 => 0
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => 0
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => 0
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [[3,2,1],[3,2],[3]]
 => 0
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [[3,2,1],[3,2],[2]]
 => 0
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [[3,2,1],[3,1],[3]]
 => 0
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [[3,2,1],[3,1],[2]]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [[3,2,1],[2,1],[2]]
 => 0
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [[3,2,1],[3,1],[1]]
 => 0
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [[3,2,1],[2,1],[1]]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,3],[4]]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,3],[3]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,2],[4]]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,2],[3]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[3,2],[3]]
 => 0
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,2],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,2],[2]]
 => 0
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[3,2],[2]]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,3],[4]]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,3],[3]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,2],[4]]
 => 1
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,2],[3]]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,3],[2,2,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,2],[3]]
 => 1
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,2],[2,2,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,2],[2]]
 => 1
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,3],[2,2,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,2],[2]]
 => 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,2],[4]]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,2],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,2],[3]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,3],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[3,2],[3]]
 => 1
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,2],[3]]
 => 0
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,2],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,2],[2]]
 => 0
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,3],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[3,2],[2]]
 => 1
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,2],[2]]
 => 0
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,1],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[4]]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,2],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[3]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,3],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,1],[3]]
 => 0
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,2],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[2]]
 => 1
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,3],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,1],[2]]
 => 1
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[4]]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,2],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[3]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[3,1],[3]]
 => 1
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,1],[3]]
 => 0
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,2],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[2]]
 => 1
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[3,1],[2]]
 => 2
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,1],[2]]
 => 1
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[2,1],[2]]
 => 0
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[2,1],[2]]
 => 0
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,2],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[1]]
 => 0
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,3],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,1],[1]]
 => 0
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,2],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[1]]
 => 0
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[3,1],[1]]
 => 1
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,1],[1]]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,4],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,4],[4]]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,3],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,3],[4]]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[4,3],[4]]
 => ? = 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,3],[3]]
 => ? = 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[4,3],[3]]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,4],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,4],[4]]
 => ? = 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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,3],[5]]
 => ? = 1
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,3],[4]]
 => ? = 2
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[4,3],[4]]
 => ? = 1
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,3],[3]]
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[4,3],[3]]
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,3],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,3],[4]]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[4,3],[4]]
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,3],[4]]
 => ? = 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,3],[3]]
 => ? = 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,3],[3]]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,2],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,2],[4]]
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[4,2],[4]]
 => ? = 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]]
 => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,2],[3]]
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,2],[5]]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,2],[4]]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,2],[4]]
 => ? = 0
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[4,2],[3]]
 => ? = 2
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[3,2],[3]]
 => ? = 0
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[3,2],[3]]
 => ? = 0
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,2],[2]]
 => ? = 0
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[4,2],[2]]
 => ? = 0
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,2],[2]]
 => ? = 0
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ? = 1
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,2],[2]]
 => ? = 0
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[3,2],[2]]
 => ? = 0
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
 => [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[3,2],[2]]
 => ? = 0
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,4],[5]]
 => ? = 0
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,4],[4]]
 => ? = 0
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,3],[5]]
 => ? = 0
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,3],[4]]
 => ? = 1
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[4,3],[4]]
 => ? = 0
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,3],[3]]
 => ? = 0
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[4,3],[3]]
 => ? = 0
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,2],[5,4],[5]]
 => ? = 1
Description
The number of special entries. An entry $a_{i,j}$ of a Gelfand-Tsetlin pattern is special if $a_{i-1,j-i} > a_{i,j} > a_{i-1,j}$. That is, it is neither boxed nor circled.
Matching statistic: St001526
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001526: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => 2 = 0 + 2
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3 = 1 + 2
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,3],[3,3],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,2],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 + 2
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2 + 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,2],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 + 2
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,2],[2,2,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,2],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,1],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,3],[2,3,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 + 2
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,3],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2 + 2
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,4],[2,3,4],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 + 2
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,2],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,2],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 2 = 0 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [5,3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2 + 2
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1 + 2
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 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]]
 => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 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]]
 => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[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]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[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]]
 => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[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]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[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]]
 => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1 + 2
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2 + 2
Description
The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001195
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => ? = 0
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,3],[3,3],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,2],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [[1,1,1,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,2],[2,2,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [[1,1,2,3],[2,2,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,2],[2,2,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,2],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,3],[2,2,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,1],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,2],[2,3,3],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => [[1,1,2,3],[2,3,3],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,2],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,3],[2,3,4],[3,4],[4]]
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => [[1,1,2,4],[2,3,4],[3,4],[4]]
 => [4,2,2,2]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,2],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,3],[2,3,3],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,2],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,3],[2,3,4],[3,4],[4]]
 => [3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,3],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,4],[2,3,4],[3,4],[4]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 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]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [5,3,3,3,1]
 => [1,1,0,1,0,0,1,1,1,0,0,1,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 2
[[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]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,4,2,1]
 => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 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]]
 => [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 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]]
 => [[1,1,1,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[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]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[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]]
 => [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [4,4,3,3,1]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
 => ? = 1
[[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]]
 => [[1,1,1,1,3],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]
 => ?
 => ?
 => ? = 1
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.