Identifier
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
[[0,0,1,0],[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],[0,0,0,1],[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
[[0,0,0,1],[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
[[0,0,0,1],[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
[[0,0,1,0],[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
[[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
[[0,0,0,1],[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
[[0,0,1,0],[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
[[0,0,0,1],[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
[[0,0,1,0,0],[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],[0,0,0,1,0],[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
[[0,0,0,1,0],[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
[[0,0,0,1,0],[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
[[0,0,1,0,0],[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
[[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
[[0,0,0,1,0],[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
[[0,0,1,0,0],[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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[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] => [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],[0,0,0,0,1],[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] => [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],[0,0,0,0,1],[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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[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] => [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],[0,0,0,0,1],[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] => [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],[0,0,0,0,1],[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] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[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]] => [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],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,2,2],[2,2,2,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => [[1,1,1,2,5],[2,2,2,5],[3,3,5],[4,5],[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],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]] => [[1,1,1,3,5],[2,2,3,5],[3,3,5],[4,5],[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],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,2],[2,2,3,3],[3,3,5],[4,5],[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],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,3],[2,2,3,3],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,2],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,2,5],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => [[1,1,2,3,5],[2,2,3,5],[3,3,5],[4,5],[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],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[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],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,1,4],[2,2,2,4],[3,4,4],[4,5],[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],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,2,2],[2,2,2,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0]] => [[1,1,1,2,4],[2,2,2,4],[3,4,4],[4,5],[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],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[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],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,1,5],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,2,2],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => [[1,1,1,2,5],[2,2,2,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0]] => [[1,1,1,4,5],[2,2,4,5],[3,4,5],[4,5],[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],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
>>> Load all 154 entries. <<<
[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,2],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,2,5],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0]] => [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[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],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,1,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0]] => [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[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],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,3],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,1,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0]] => [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,1,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0]] => [[1,1,1,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0]] => [[1,1,3,4,5],[2,3,4,5],[3,4,5],[4,5],[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],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,3],[3,4,4],[4,5],[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],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,3],[2,3,3,3],[3,4,4],[4,5],[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],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,2,4],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => [[1,2,2,3,4],[2,3,3,4],[3,4,4],[4,5],[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],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,3],[3,4,5],[4,5],[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],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,3],[2,3,3,3],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,2,5],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => [[1,2,2,3,5],[2,3,3,5],[3,4,5],[4,5],[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],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,2],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,2,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => [[1,2,2,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
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 www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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
weight
Description
The weight of a semistandard tableau as an integer partition.
The weight (or content) of a semistandard tableaux $T$ with maximal entry $m$ is the weak composition $(\alpha_1, \dots, \alpha_m)$ such that $\alpha_i$ is the number of letters $i$ occurring in $T$.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.