Identifier
Values
[2,1] => [[0,1],[1,0]] => [[1,2],[2]] => ([(0,1)],2) => 1
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]] => [[1,1,1],[2,3],[3]] => ([(0,1)],2) => 1
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]] => [[1,1,2],[2,2],[3]] => ([(0,1)],2) => 1
[2,3,1] => [[0,0,1],[1,0,0],[0,1,0]] => [[1,1,3],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,2] => [[0,1,0],[0,0,1],[1,0,0]] => [[1,2,2],[2,3],[3]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,4,3] => [[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]] => ([(0,1)],2) => 1
[1,3,2,4] => [[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]] => ([(0,1)],2) => 1
[1,3,4,2] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,4,2,3] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,3,4] => [[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]] => ([(0,1)],2) => 1
[2,1,4,3] => [[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]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,3,1,4] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,2,4] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,3,5,4] => [[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]] => ([(0,1)],2) => 1
[1,2,4,3,5] => [[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]] => ([(0,1)],2) => 1
[1,2,4,5,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,3,2,4,5] => [[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]] => ([(0,1)],2) => 1
[1,3,2,5,4] => [[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]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,3,4,2,5] => [[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]] => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,4,2,3,5] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,3,4,5] => [[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]] => ([(0,1)],2) => 1
[2,1,3,5,4] => [[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]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,1,4,3,5] => [[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]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,3,1,4,5] => [[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]] => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,2,4,5] => [[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]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1)],2) => 1
[1,2,3,5,4,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1)],2) => 1
[1,2,3,5,6,4] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,4,3,5,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1)],2) => 1
[1,2,4,3,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,2,4,5,3,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => 1
[1,3,2,4,5,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => 1
[1,3,2,4,6,5] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,3,2,5,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,3,4,2,5,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,3,4,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => 1
[2,1,3,4,6,5] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,1,3,5,4,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,1,4,3,5,6] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,3,1,4,5,6] => [[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,3),(2,1),(3,2)],4) => 1
search for individual values
searching the database for the individual values of this statistic
Description
The size of the automorphism group of a poset.
A poset automorphism is a permutation of the elements of the poset preserving the order relation.
Map
to semistandard tableau via monotone triangles
Description
The semistandard tableau corresponding the monotone triangle of an alternating sign matrix.
This is obtained by interpreting each row of the monotone triangle as an integer partition, and filling the cells of the smallest partition with ones, the second smallest with twos, and so on.
Map
to alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.