searching the database
Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000197
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
St000197: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> 1
[[1,0],[0,1]]
=> 2
[[0,1],[1,0]]
=> 2
[[1,0,0],[0,1,0],[0,0,1]]
=> 3
[[0,1,0],[1,0,0],[0,0,1]]
=> 3
[[1,0,0],[0,0,1],[0,1,0]]
=> 3
[[0,1,0],[1,-1,1],[0,1,0]]
=> 4
[[0,0,1],[1,0,0],[0,1,0]]
=> 3
[[0,1,0],[0,0,1],[1,0,0]]
=> 3
[[0,0,1],[0,1,0],[1,0,0]]
=> 3
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> 4
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> 4
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> 4
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> 5
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
=> 4
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
=> 4
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
=> 4
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> 4
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> 4
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
=> 5
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
=> 6
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
=> 5
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
=> 5
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> 5
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
=> 4
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
=> 5
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
=> 5
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
=> 4
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> 4
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
=> 5
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
=> 4
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
=> 4
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
=> 5
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> 4
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
=> 5
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
=> 5
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
=> 4
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
=> 5
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
=> 5
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
=> 4
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
=> 5
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
=> 6
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
=> 5
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
=> 4
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
=> 4
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
=> 4
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
=> 4
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> 4
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
=> 5
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> 4
Description
The number of entries equal to positive one in the alternating sign matrix.
Matching statistic: St000176
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000176: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000176: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Values
[[1]]
=> [[1]]
=> [[1]]
=> 1
[[1,0],[0,1]]
=> [[1,1],[2]]
=> [[2,1],[2]]
=> 2
[[0,1],[1,0]]
=> [[1,2],[2]]
=> [[2,1],[1]]
=> 2
[[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> [[3,2,1],[3,2],[3]]
=> 3
[[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> [[3,2,1],[3,2],[2]]
=> 3
[[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> [[3,2,1],[3,1],[3]]
=> 3
[[0,1,0],[1,-1,1],[0,1,0]]
=> [[1,1,2],[2,3],[3]]
=> [[3,2,1],[3,1],[2]]
=> 4
[[0,0,1],[1,0,0],[0,1,0]]
=> [[1,1,3],[2,3],[3]]
=> [[3,2,1],[2,1],[2]]
=> 3
[[0,1,0],[0,0,1],[1,0,0]]
=> [[1,2,2],[2,3],[3]]
=> [[3,2,1],[3,1],[1]]
=> 3
[[0,0,1],[0,1,0],[1,0,0]]
=> [[1,2,3],[2,3],[3]]
=> [[3,2,1],[2,1],[1]]
=> 3
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 6
[[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]]
=> 5
[[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]]
=> 5
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 6
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 4
[[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]]
=> 5
[[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]]
=> 4
[[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 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]]
=> [[1,1,1,1,1],[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,2,2],[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]]
=> ? = 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]]
=> [[1,1,1,2,3],[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]]
=> ? = 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]]
=> [[1,1,1,1,1],[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 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]]
=> [[1,1,1,1,1],[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]]
=> ? = 6
[[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]]
=> ? = 7
[[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]]
=> ? = 6
[[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]]
=> ? = 6
[[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]]
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 6
[[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]]
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,2,2],[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]]
=> ? = 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]]
=> [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ?
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,1,1],[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,2,2],[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]]
=> ? = 6
[[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]]
=> ?
=> ? = 6
[[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]]
=> ? = 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]]
=> [[1,1,1,1,2],[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]]
=> ? = 6
[[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]]
=> ?
=> ? = 6
[[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]]
=> ? = 5
[[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]]
=> ?
=> ? = 6
[[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]]
=> ? = 7
[[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]]
=> ?
=> ? = 6
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ?
=> ? = 6
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 6
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 5
[[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]]
=> ? = 6
Description
The total number of tiles in the Gelfand-Tsetlin pattern.
The tiling of a Gelfand-Tsetlin pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called tiles, and each entry in a pattern belongs to exactly one tile.
Matching statistic: St001515
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
St001515: Dyck paths ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 44%
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001515: Dyck paths ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 44%
Values
[[1]]
=> [[1]]
=> [1]
=> [1,0,1,0]
=> 1
[[1,0],[0,1]]
=> [[1,1],[2]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[[0,1],[1,0]]
=> [[1,2],[2]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 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]
=> 3
[[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]
=> 3
[[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]
=> 3
[[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]
=> 4
[[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]
=> 3
[[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]
=> 3
[[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]
=> 3
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> ? = 6
[[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]
=> ? = 5
[[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]
=> ? = 5
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> ? = 6
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 5
[[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]
=> 4
[[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]
=> 4
[[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]
=> 4
[[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]
=> ? = 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]]
=> [[1,1,1,1,2],[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]
=> ? = 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]]
=> [[1,1,1,1,1],[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]
=> ? = 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]]
=> [[1,1,1,1,2],[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]
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,2,2],[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]
=> ? = 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]]
=> [[1,1,1,2,3],[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]
=> ? = 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]]
=> [[1,1,1,1,1],[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]
=> ? = 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]]
=> [[1,1,1,1,2],[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]
=> ? = 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]]
=> [[1,1,1,1,1],[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]
=> ? = 6
[[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]
=> ? = 7
[[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]
=> ? = 6
[[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]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,1,2],[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]
=> ? = 6
[[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]
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,2,2],[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]
=> ? = 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]]
=> [[1,1,1,2,3],[2,2,2,4],[3,3,4],[4,4],[5]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,1,1],[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]
=> ? = 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]]
=> [[1,1,1,1,2],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]
=> ?
=> ?
=> ? = 6
[[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]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 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]]
=> [[1,1,1,1,2],[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]
=> ? = 6
[[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]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 5
[[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]]
=> ?
=> ?
=> ? = 6
[[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]
=> ? = 7
Description
The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule).
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!