Identifier
Values
[[1,2]] => [[1,2]] => 1
[[2,2]] => [[2,2]] => 2
[[1],[2]] => [[1,2]] => 1
[[1,3]] => [[1,3]] => 1
[[2,3]] => [[2,3]] => 2
[[3,3]] => [[3,3]] => 3
[[1],[3]] => [[1,3]] => 1
[[2],[3]] => [[2,3]] => 2
[[1,1,2]] => [[1,1,2]] => 1
[[1,2,2]] => [[1,2,2]] => 1
[[2,2,2]] => [[2,2,2]] => 2
[[1,1],[2]] => [[1,1,2]] => 1
[[1,2],[2]] => [[1,2,2]] => 1
[[1,4]] => [[1,4]] => 1
[[2,4]] => [[2,4]] => 2
[[3,4]] => [[3,4]] => 3
[[4,4]] => [[4,4]] => 4
[[1],[4]] => [[1,4]] => 1
[[2],[4]] => [[2,4]] => 2
[[3],[4]] => [[3,4]] => 3
[[1,1,3]] => [[1,1,3]] => 1
[[1,2,3]] => [[1,2,3]] => 1
[[1,3,3]] => [[1,3,3]] => 1
[[2,2,3]] => [[2,2,3]] => 2
[[2,3,3]] => [[2,3,3]] => 2
[[3,3,3]] => [[3,3,3]] => 3
[[1,1],[3]] => [[1,1,3]] => 1
[[1,2],[3]] => [[1,2,3]] => 1
[[1,3],[2]] => [[1,2],[3]] => 1
[[1,3],[3]] => [[1,3,3]] => 1
[[2,2],[3]] => [[2,2,3]] => 2
[[2,3],[3]] => [[2,3,3]] => 2
[[1],[2],[3]] => [[1,2],[3]] => 1
[[1,1,1,2]] => [[1,1,1,2]] => 1
[[1,1,2,2]] => [[1,1,2,2]] => 1
[[1,2,2,2]] => [[1,2,2,2]] => 1
[[2,2,2,2]] => [[2,2,2,2]] => 2
[[1,1,1],[2]] => [[1,1,1,2]] => 1
[[1,1,2],[2]] => [[1,1,2,2]] => 1
[[1,2,2],[2]] => [[1,2,2,2]] => 1
[[1,1],[2,2]] => [[1,1,2,2]] => 1
[[1,5]] => [[1,5]] => 1
[[2,5]] => [[2,5]] => 2
[[3,5]] => [[3,5]] => 3
[[4,5]] => [[4,5]] => 4
[[5,5]] => [[5,5]] => 5
[[1],[5]] => [[1,5]] => 1
[[2],[5]] => [[2,5]] => 2
[[3],[5]] => [[3,5]] => 3
[[4],[5]] => [[4,5]] => 4
[[1,1,4]] => [[1,1,4]] => 1
[[1,2,4]] => [[1,2,4]] => 1
[[1,3,4]] => [[1,3,4]] => 1
[[1,4,4]] => [[1,4,4]] => 1
[[2,2,4]] => [[2,2,4]] => 2
[[2,3,4]] => [[2,3,4]] => 2
[[2,4,4]] => [[2,4,4]] => 2
[[3,3,4]] => [[3,3,4]] => 3
[[3,4,4]] => [[3,4,4]] => 3
[[4,4,4]] => [[4,4,4]] => 4
[[1,1],[4]] => [[1,1,4]] => 1
[[1,2],[4]] => [[1,2,4]] => 1
[[1,4],[2]] => [[1,2],[4]] => 1
[[1,3],[4]] => [[1,3,4]] => 1
[[1,4],[3]] => [[1,3],[4]] => 1
[[1,4],[4]] => [[1,4,4]] => 1
[[2,2],[4]] => [[2,2,4]] => 2
[[2,3],[4]] => [[2,3,4]] => 2
[[2,4],[3]] => [[2,3],[4]] => 2
[[2,4],[4]] => [[2,4,4]] => 2
[[3,3],[4]] => [[3,3,4]] => 3
[[3,4],[4]] => [[3,4,4]] => 3
[[1],[2],[4]] => [[1,2],[4]] => 1
[[1],[3],[4]] => [[1,3],[4]] => 1
[[2],[3],[4]] => [[2,3],[4]] => 2
[[1,1,1,3]] => [[1,1,1,3]] => 1
[[1,1,2,3]] => [[1,1,2,3]] => 1
[[1,1,3,3]] => [[1,1,3,3]] => 1
[[1,2,2,3]] => [[1,2,2,3]] => 1
[[1,2,3,3]] => [[1,2,3,3]] => 1
[[1,3,3,3]] => [[1,3,3,3]] => 1
[[2,2,2,3]] => [[2,2,2,3]] => 2
[[2,2,3,3]] => [[2,2,3,3]] => 2
[[2,3,3,3]] => [[2,3,3,3]] => 2
[[3,3,3,3]] => [[3,3,3,3]] => 3
[[1,1,1],[3]] => [[1,1,1,3]] => 1
[[1,1,2],[3]] => [[1,1,2,3]] => 1
[[1,1,3],[2]] => [[1,1,2],[3]] => 1
[[1,1,3],[3]] => [[1,1,3,3]] => 1
[[1,2,2],[3]] => [[1,2,2,3]] => 1
[[1,2,3],[2]] => [[1,2,2],[3]] => 1
[[1,2,3],[3]] => [[1,2,3,3]] => 1
[[1,3,3],[2]] => [[1,2,3],[3]] => 1
[[1,3,3],[3]] => [[1,3,3,3]] => 1
[[2,2,2],[3]] => [[2,2,2,3]] => 2
[[2,2,3],[3]] => [[2,2,3,3]] => 2
[[2,3,3],[3]] => [[2,3,3,3]] => 2
[[1,1],[2,3]] => [[1,1,2,3]] => 1
[[1,1],[3,3]] => [[1,1,3,3]] => 1
[[1,2],[2,3]] => [[1,2,2,3]] => 1
[[1,2],[3,3]] => [[1,2,3,3]] => 1
>>> Load all 499 entries. <<<
[[2,2],[3,3]] => [[2,2,3,3]] => 2
[[1,1],[2],[3]] => [[1,1,2],[3]] => 1
[[1,2],[2],[3]] => [[1,2,2],[3]] => 1
[[1,3],[2],[3]] => [[1,2,3],[3]] => 1
[[1,1,1,1,2]] => [[1,1,1,1,2]] => 1
[[1,1,1,2,2]] => [[1,1,1,2,2]] => 1
[[1,1,2,2,2]] => [[1,1,2,2,2]] => 1
[[1,2,2,2,2]] => [[1,2,2,2,2]] => 1
[[2,2,2,2,2]] => [[2,2,2,2,2]] => 2
[[1,1,1,1],[2]] => [[1,1,1,1,2]] => 1
[[1,1,1,2],[2]] => [[1,1,1,2,2]] => 1
[[1,1,2,2],[2]] => [[1,1,2,2,2]] => 1
[[1,2,2,2],[2]] => [[1,2,2,2,2]] => 1
[[1,1,1],[2,2]] => [[1,1,1,2,2]] => 1
[[1,1,2],[2,2]] => [[1,1,2,2,2]] => 1
[[1,6]] => [[1,6]] => 1
[[2,6]] => [[2,6]] => 2
[[3,6]] => [[3,6]] => 3
[[4,6]] => [[4,6]] => 4
[[5,6]] => [[5,6]] => 5
[[6,6]] => [[6,6]] => 6
[[1],[6]] => [[1,6]] => 1
[[2],[6]] => [[2,6]] => 2
[[3],[6]] => [[3,6]] => 3
[[4],[6]] => [[4,6]] => 4
[[5],[6]] => [[5,6]] => 5
[[1,1,5]] => [[1,1,5]] => 1
[[1,2,5]] => [[1,2,5]] => 1
[[1,3,5]] => [[1,3,5]] => 1
[[1,4,5]] => [[1,4,5]] => 1
[[1,5,5]] => [[1,5,5]] => 1
[[2,2,5]] => [[2,2,5]] => 2
[[2,3,5]] => [[2,3,5]] => 2
[[2,4,5]] => [[2,4,5]] => 2
[[2,5,5]] => [[2,5,5]] => 2
[[3,3,5]] => [[3,3,5]] => 3
[[3,4,5]] => [[3,4,5]] => 3
[[3,5,5]] => [[3,5,5]] => 3
[[4,4,5]] => [[4,4,5]] => 4
[[4,5,5]] => [[4,5,5]] => 4
[[5,5,5]] => [[5,5,5]] => 5
[[1,1],[5]] => [[1,1,5]] => 1
[[1,2],[5]] => [[1,2,5]] => 1
[[1,5],[2]] => [[1,2],[5]] => 1
[[1,3],[5]] => [[1,3,5]] => 1
[[1,5],[3]] => [[1,3],[5]] => 1
[[1,4],[5]] => [[1,4,5]] => 1
[[1,5],[4]] => [[1,4],[5]] => 1
[[1,5],[5]] => [[1,5,5]] => 1
[[2,2],[5]] => [[2,2,5]] => 2
[[2,3],[5]] => [[2,3,5]] => 2
[[2,5],[3]] => [[2,3],[5]] => 2
[[2,4],[5]] => [[2,4,5]] => 2
[[2,5],[4]] => [[2,4],[5]] => 2
[[2,5],[5]] => [[2,5,5]] => 2
[[3,3],[5]] => [[3,3,5]] => 3
[[3,4],[5]] => [[3,4,5]] => 3
[[3,5],[4]] => [[3,4],[5]] => 3
[[3,5],[5]] => [[3,5,5]] => 3
[[4,4],[5]] => [[4,4,5]] => 4
[[4,5],[5]] => [[4,5,5]] => 4
[[1],[2],[5]] => [[1,2],[5]] => 1
[[1],[3],[5]] => [[1,3],[5]] => 1
[[1],[4],[5]] => [[1,4],[5]] => 1
[[2],[3],[5]] => [[2,3],[5]] => 2
[[2],[4],[5]] => [[2,4],[5]] => 2
[[3],[4],[5]] => [[3,4],[5]] => 3
[[1,1,1,4]] => [[1,1,1,4]] => 1
[[1,1,2,4]] => [[1,1,2,4]] => 1
[[1,1,3,4]] => [[1,1,3,4]] => 1
[[1,1,4,4]] => [[1,1,4,4]] => 1
[[1,2,2,4]] => [[1,2,2,4]] => 1
[[1,2,3,4]] => [[1,2,3,4]] => 1
[[1,2,4,4]] => [[1,2,4,4]] => 1
[[1,3,3,4]] => [[1,3,3,4]] => 1
[[1,3,4,4]] => [[1,3,4,4]] => 1
[[1,4,4,4]] => [[1,4,4,4]] => 1
[[2,2,2,4]] => [[2,2,2,4]] => 2
[[2,2,3,4]] => [[2,2,3,4]] => 2
[[2,2,4,4]] => [[2,2,4,4]] => 2
[[2,3,3,4]] => [[2,3,3,4]] => 2
[[2,3,4,4]] => [[2,3,4,4]] => 2
[[2,4,4,4]] => [[2,4,4,4]] => 2
[[3,3,3,4]] => [[3,3,3,4]] => 3
[[3,3,4,4]] => [[3,3,4,4]] => 3
[[3,4,4,4]] => [[3,4,4,4]] => 3
[[4,4,4,4]] => [[4,4,4,4]] => 4
[[1,1,1],[4]] => [[1,1,1,4]] => 1
[[1,1,2],[4]] => [[1,1,2,4]] => 1
[[1,1,4],[2]] => [[1,1,2],[4]] => 1
[[1,1,3],[4]] => [[1,1,3,4]] => 1
[[1,1,4],[3]] => [[1,1,3],[4]] => 1
[[1,1,4],[4]] => [[1,1,4,4]] => 1
[[1,2,2],[4]] => [[1,2,2,4]] => 1
[[1,2,4],[2]] => [[1,2,2],[4]] => 1
[[1,2,3],[4]] => [[1,2,3,4]] => 1
[[1,2,4],[3]] => [[1,2,3],[4]] => 1
[[1,3,4],[2]] => [[1,2,4],[3]] => 1
[[1,2,4],[4]] => [[1,2,4,4]] => 1
[[1,4,4],[2]] => [[1,2,4],[4]] => 1
[[1,3,3],[4]] => [[1,3,3,4]] => 1
[[1,3,4],[3]] => [[1,3,3],[4]] => 1
[[1,3,4],[4]] => [[1,3,4,4]] => 1
[[1,4,4],[3]] => [[1,3,4],[4]] => 1
[[1,4,4],[4]] => [[1,4,4,4]] => 1
[[2,2,2],[4]] => [[2,2,2,4]] => 2
[[2,2,3],[4]] => [[2,2,3,4]] => 2
[[2,2,4],[3]] => [[2,2,3],[4]] => 2
[[2,2,4],[4]] => [[2,2,4,4]] => 2
[[2,3,3],[4]] => [[2,3,3,4]] => 2
[[2,3,4],[3]] => [[2,3,3],[4]] => 2
[[2,3,4],[4]] => [[2,3,4,4]] => 2
[[2,4,4],[3]] => [[2,3,4],[4]] => 2
[[2,4,4],[4]] => [[2,4,4,4]] => 2
[[3,3,3],[4]] => [[3,3,3,4]] => 3
[[3,3,4],[4]] => [[3,3,4,4]] => 3
[[3,4,4],[4]] => [[3,4,4,4]] => 3
[[1,1],[2,4]] => [[1,1,2,4]] => 1
[[1,1],[3,4]] => [[1,1,3,4]] => 1
[[1,1],[4,4]] => [[1,1,4,4]] => 1
[[1,2],[2,4]] => [[1,2,2,4]] => 1
[[1,2],[3,4]] => [[1,2,3,4]] => 1
[[1,3],[2,4]] => [[1,2,4],[3]] => 1
[[1,2],[4,4]] => [[1,2,4,4]] => 1
[[1,3],[3,4]] => [[1,3,3,4]] => 1
[[1,3],[4,4]] => [[1,3,4,4]] => 1
[[2,2],[3,4]] => [[2,2,3,4]] => 2
[[2,2],[4,4]] => [[2,2,4,4]] => 2
[[2,3],[3,4]] => [[2,3,3,4]] => 2
[[2,3],[4,4]] => [[2,3,4,4]] => 2
[[3,3],[4,4]] => [[3,3,4,4]] => 3
[[1,1],[2],[4]] => [[1,1,2],[4]] => 1
[[1,1],[3],[4]] => [[1,1,3],[4]] => 1
[[1,2],[2],[4]] => [[1,2,2],[4]] => 1
[[1,2],[3],[4]] => [[1,2,3],[4]] => 1
[[1,3],[2],[4]] => [[1,2,4],[3]] => 1
[[1,4],[2],[3]] => [[1,2],[3],[4]] => 1
[[1,4],[2],[4]] => [[1,2,4],[4]] => 1
[[1,3],[3],[4]] => [[1,3,3],[4]] => 1
[[1,4],[3],[4]] => [[1,3,4],[4]] => 1
[[2,2],[3],[4]] => [[2,2,3],[4]] => 2
[[2,3],[3],[4]] => [[2,3,3],[4]] => 2
[[2,4],[3],[4]] => [[2,3,4],[4]] => 2
[[1],[2],[3],[4]] => [[1,2],[3],[4]] => 1
[[1,1,1,1,3]] => [[1,1,1,1,3]] => 1
[[1,1,1,2,3]] => [[1,1,1,2,3]] => 1
[[1,1,1,3,3]] => [[1,1,1,3,3]] => 1
[[1,1,2,2,3]] => [[1,1,2,2,3]] => 1
[[1,1,2,3,3]] => [[1,1,2,3,3]] => 1
[[1,1,3,3,3]] => [[1,1,3,3,3]] => 1
[[1,2,2,2,3]] => [[1,2,2,2,3]] => 1
[[1,2,2,3,3]] => [[1,2,2,3,3]] => 1
[[1,2,3,3,3]] => [[1,2,3,3,3]] => 1
[[1,3,3,3,3]] => [[1,3,3,3,3]] => 1
[[2,2,2,2,3]] => [[2,2,2,2,3]] => 2
[[2,2,2,3,3]] => [[2,2,2,3,3]] => 2
[[2,2,3,3,3]] => [[2,2,3,3,3]] => 2
[[2,3,3,3,3]] => [[2,3,3,3,3]] => 2
[[3,3,3,3,3]] => [[3,3,3,3,3]] => 3
[[1,1,1,1],[3]] => [[1,1,1,1,3]] => 1
[[1,1,1,2],[3]] => [[1,1,1,2,3]] => 1
[[1,1,1,3],[2]] => [[1,1,1,2],[3]] => 1
[[1,1,1,3],[3]] => [[1,1,1,3,3]] => 1
[[1,1,2,2],[3]] => [[1,1,2,2,3]] => 1
[[1,1,2,3],[2]] => [[1,1,2,2],[3]] => 1
[[1,1,2,3],[3]] => [[1,1,2,3,3]] => 1
[[1,1,3,3],[2]] => [[1,1,2,3],[3]] => 1
[[1,1,3,3],[3]] => [[1,1,3,3,3]] => 1
[[1,2,2,2],[3]] => [[1,2,2,2,3]] => 1
[[1,2,2,3],[2]] => [[1,2,2,2],[3]] => 1
[[1,2,2,3],[3]] => [[1,2,2,3,3]] => 1
[[1,2,3,3],[2]] => [[1,2,2,3],[3]] => 1
[[1,2,3,3],[3]] => [[1,2,3,3,3]] => 1
[[1,3,3,3],[2]] => [[1,2,3,3],[3]] => 1
[[1,3,3,3],[3]] => [[1,3,3,3,3]] => 1
[[2,2,2,2],[3]] => [[2,2,2,2,3]] => 2
[[2,2,2,3],[3]] => [[2,2,2,3,3]] => 2
[[2,2,3,3],[3]] => [[2,2,3,3,3]] => 2
[[2,3,3,3],[3]] => [[2,3,3,3,3]] => 2
[[1,1,1],[2,3]] => [[1,1,1,2,3]] => 1
[[1,1,1],[3,3]] => [[1,1,1,3,3]] => 1
[[1,1,2],[2,3]] => [[1,1,2,2,3]] => 1
[[1,1,3],[2,2]] => [[1,1,2,2],[3]] => 1
[[1,1,2],[3,3]] => [[1,1,2,3,3]] => 1
[[1,1,3],[2,3]] => [[1,1,2,3],[3]] => 1
[[1,1,3],[3,3]] => [[1,1,3,3,3]] => 1
[[1,2,2],[2,3]] => [[1,2,2,2,3]] => 1
[[1,2,2],[3,3]] => [[1,2,2,3,3]] => 1
[[1,2,3],[2,3]] => [[1,2,2,3],[3]] => 1
[[1,2,3],[3,3]] => [[1,2,3,3,3]] => 1
[[2,2,2],[3,3]] => [[2,2,2,3,3]] => 2
[[2,2,3],[3,3]] => [[2,2,3,3,3]] => 2
[[1,1,1],[2],[3]] => [[1,1,1,2],[3]] => 1
[[1,1,2],[2],[3]] => [[1,1,2,2],[3]] => 1
[[1,1,3],[2],[3]] => [[1,1,2,3],[3]] => 1
[[1,2,2],[2],[3]] => [[1,2,2,2],[3]] => 1
[[1,2,3],[2],[3]] => [[1,2,2,3],[3]] => 1
[[1,3,3],[2],[3]] => [[1,2,3,3],[3]] => 1
[[1,1],[2,2],[3]] => [[1,1,2,2],[3]] => 1
[[1,1],[2,3],[3]] => [[1,1,2,3],[3]] => 1
[[1,2],[2,3],[3]] => [[1,2,2,3],[3]] => 1
[[1,1,1,1,1,2]] => [[1,1,1,1,1,2]] => 1
[[1,1,1,1,2,2]] => [[1,1,1,1,2,2]] => 1
[[1,1,1,2,2,2]] => [[1,1,1,2,2,2]] => 1
[[1,1,2,2,2,2]] => [[1,1,2,2,2,2]] => 1
[[1,2,2,2,2,2]] => [[1,2,2,2,2,2]] => 1
[[2,2,2,2,2,2]] => [[2,2,2,2,2,2]] => 2
[[1,1,1,1,1],[2]] => [[1,1,1,1,1,2]] => 1
[[1,1,1,1,2],[2]] => [[1,1,1,1,2,2]] => 1
[[1,1,1,2,2],[2]] => [[1,1,1,2,2,2]] => 1
[[1,1,2,2,2],[2]] => [[1,1,2,2,2,2]] => 1
[[1,2,2,2,2],[2]] => [[1,2,2,2,2,2]] => 1
[[1,1,1,1],[2,2]] => [[1,1,1,1,2,2]] => 1
[[1,1,1,2],[2,2]] => [[1,1,1,2,2,2]] => 1
[[1,1,2,2],[2,2]] => [[1,1,2,2,2,2]] => 1
[[1,1,1],[2,2,2]] => [[1,1,1,2,2,2]] => 1
[[1,1,1,2,3],[2]] => [[1,1,1,2,2],[3]] => 1
[[1,1,1,3,3],[2]] => [[1,1,1,2,3],[3]] => 1
[[1,1,2,2,3],[2]] => [[1,1,2,2,2],[3]] => 1
[[1,1,2,3,3],[2]] => [[1,1,2,2,3],[3]] => 1
[[1,1,3,3,3],[2]] => [[1,1,2,3,3],[3]] => 1
[[1,2,2,3,3],[2]] => [[1,2,2,2,3],[3]] => 1
[[1,2,3,3,3],[2]] => [[1,2,2,3,3],[3]] => 1
[[1,1,1,3],[2,2]] => [[1,1,1,2,2],[3]] => 1
[[1,1,1,3],[2,3]] => [[1,1,1,2,3],[3]] => 1
[[1,1,2,3],[2,2]] => [[1,1,2,2,2],[3]] => 1
[[1,1,2,3],[2,3]] => [[1,1,2,2,3],[3]] => 1
[[1,1,3,3],[2,3]] => [[1,1,2,3,3],[3]] => 1
[[1,2,2,3],[2,3]] => [[1,2,2,2,3],[3]] => 1
[[1,2,3,3],[2,3]] => [[1,2,2,3,3],[3]] => 1
[[1,1,1,2],[2],[3]] => [[1,1,1,2,2],[3]] => 1
[[1,1,1,3],[2],[3]] => [[1,1,1,2,3],[3]] => 1
[[1,1,2,2],[2],[3]] => [[1,1,2,2,2],[3]] => 1
[[1,1,2,3],[2],[3]] => [[1,1,2,2,3],[3]] => 1
[[1,1,3,3],[2],[3]] => [[1,1,2,3,3],[3]] => 1
[[1,2,2,3],[2],[3]] => [[1,2,2,2,3],[3]] => 1
[[1,2,3,3],[2],[3]] => [[1,2,2,3,3],[3]] => 1
[[1,1,1],[2,2],[3]] => [[1,1,1,2,2],[3]] => 1
[[1,1,1],[2,3],[3]] => [[1,1,1,2,3],[3]] => 1
[[1,1,2],[2,2],[3]] => [[1,1,2,2,2],[3]] => 1
[[1,1,2],[2,3],[3]] => [[1,1,2,2,3],[3]] => 1
[[1,1,3],[2,3],[3]] => [[1,1,2,3,3],[3]] => 1
[[1,2,2],[2,3],[3]] => [[1,2,2,2,3],[3]] => 1
[[1,2,3],[2,3],[3]] => [[1,2,2,3,3],[3]] => 1
[[1,2,3,4,5]] => [[1,2,3,4,5]] => 1
[[1,2,3,4],[5]] => [[1,2,3,4,5]] => 1
[[1,2,3,5],[4]] => [[1,2,3,4],[5]] => 1
[[1,2,4,5],[3]] => [[1,2,3,5],[4]] => 1
[[1,3,4,5],[2]] => [[1,2,4,5],[3]] => 1
[[1,2,3],[4,5]] => [[1,2,3,4,5]] => 1
[[1,2,4],[3,5]] => [[1,2,3,5],[4]] => 1
[[1,2,5],[3,4]] => [[1,2,3,4],[5]] => 1
[[1,3,4],[2,5]] => [[1,2,4,5],[3]] => 1
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => 6
[[1,2,3],[4],[5]] => [[1,2,3,4],[5]] => 1
[[1,2,4],[3],[5]] => [[1,2,3,5],[4]] => 1
[[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => 1
[[1,3,4],[2],[5]] => [[1,2,4,5],[3]] => 1
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 1
[[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => 1
[[1,2],[3,4],[5]] => [[1,2,3,4],[5]] => 1
[[1,2],[3,5],[4]] => [[1,2,3,5],[4]] => 1
[[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => 6
[[1,3],[2,5],[4]] => [[1,2,4,5],[3]] => 1
[[1,4],[2,5],[3]] => [[1,2,5],[3],[4]] => 1
[[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => 1
[[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => 1
[[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => 1
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => 1
[[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => 1
[[1]] => [[1]] => 1
[[1,1,1,1],[2,2,2],[3,3],[4]] => [[1,1,1,1,2,2,2],[3,3],[4]] => 4
[[1,1,1,2],[2,2,2],[3,3],[4]] => [[1,1,1,2,2,2,2],[3,3],[4]] => 4
[[1,1,1,1],[2,2,3],[3,3],[4]] => [[1,1,1,1,2,2,3],[3,3],[4]] => 4
[[1,1,1,2],[2,2,3],[3,3],[4]] => [[1,1,1,2,2,2,3],[3,3],[4]] => 4
[[1,1,1,3],[2,2,3],[3,3],[4]] => [[1,1,1,2,2,3,3],[3,3],[4]] => 4
[[1,1,2,2],[2,2,3],[3,3],[4]] => [[1,1,2,2,2,2,3],[3,3],[4]] => 4
[[1,1,2,3],[2,2,3],[3,3],[4]] => [[1,1,2,2,2,3,3],[3,3],[4]] => 4
[[1,1,1,1],[2,2,2],[3,4],[4]] => [[1,1,1,1,2,2,2],[3,4],[4]] => 5
[[1,1,1,2],[2,2,2],[3,4],[4]] => [[1,1,1,2,2,2,2],[3,4],[4]] => 5
[[1,1,1,1],[2,2,3],[3,4],[4]] => [[1,1,1,1,2,2,3],[3,4],[4]] => 5
[[1,1,1,2],[2,2,3],[3,4],[4]] => [[1,1,1,2,2,2,3],[3,4],[4]] => 5
[[1,1,1,3],[2,2,3],[3,4],[4]] => [[1,1,1,2,2,3],[3,3,4],[4]] => 4
[[1,1,2,2],[2,2,3],[3,4],[4]] => [[1,1,2,2,2,2,3],[3,4],[4]] => 5
[[1,1,2,3],[2,2,3],[3,4],[4]] => [[1,1,2,2,2,3],[3,3,4],[4]] => 4
[[1,1,1,1],[2,2,4],[3,4],[4]] => [[1,1,1,1,2,2,4],[3,4],[4]] => 5
[[1,1,1,2],[2,2,4],[3,4],[4]] => [[1,1,1,2,2,2,4],[3,4],[4]] => 5
[[1,1,1,3],[2,2,4],[3,4],[4]] => [[1,1,1,2,2,4,4],[3,3],[4]] => 4
[[1,1,1,4],[2,2,4],[3,4],[4]] => [[1,1,1,2,2,4,4],[3,4],[4]] => 5
[[1,1,2,2],[2,2,4],[3,4],[4]] => [[1,1,2,2,2,2,4],[3,4],[4]] => 5
[[1,1,2,3],[2,2,4],[3,4],[4]] => [[1,1,2,2,2,4,4],[3,3],[4]] => 4
[[1,1,2,4],[2,2,4],[3,4],[4]] => [[1,1,2,2,2,4,4],[3,4],[4]] => 5
[[1,1,1,1],[2,3,3],[3,4],[4]] => [[1,1,1,1,2,3,3],[3,4],[4]] => 5
[[1,1,1,2],[2,3,3],[3,4],[4]] => [[1,1,1,2,2,3,3],[3,4],[4]] => 5
[[1,1,1,3],[2,3,3],[3,4],[4]] => [[1,1,1,2,3,3,3],[3,4],[4]] => 5
[[1,1,2,2],[2,3,3],[3,4],[4]] => [[1,1,2,2,2,3,3],[3,4],[4]] => 5
[[1,1,2,3],[2,3,3],[3,4],[4]] => [[1,1,2,2,3,3,3],[3,4],[4]] => 5
[[1,1,1,1],[2,3,4],[3,4],[4]] => [[1,1,1,1,2,3,4],[3,4],[4]] => 5
[[1,1,1,2],[2,3,4],[3,4],[4]] => [[1,1,1,2,2,3,4],[3,4],[4]] => 5
[[1,1,1,3],[2,3,4],[3,4],[4]] => [[1,1,1,2,3,3,4],[3,4],[4]] => 5
[[1,1,1,4],[2,3,4],[3,4],[4]] => [[1,1,1,2,3,4,4],[3,4],[4]] => 5
[[1,1,2,2],[2,3,4],[3,4],[4]] => [[1,1,2,2,2,3,4],[3,4],[4]] => 5
[[1,1,2,3],[2,3,4],[3,4],[4]] => [[1,1,2,2,3,3,4],[3,4],[4]] => 5
[[1,1,2,4],[2,3,4],[3,4],[4]] => [[1,1,2,2,3,4,4],[3,4],[4]] => 5
[[1,1,3,3],[2,3,4],[3,4],[4]] => [[1,1,2,3,3,3,4],[3,4],[4]] => 5
[[1,1,3,4],[2,3,4],[3,4],[4]] => [[1,1,2,3,3,4,4],[3,4],[4]] => 5
[[1,2,2,2],[2,3,3],[3,4],[4]] => [[1,2,2,2,2,3,3],[3,4],[4]] => 5
[[1,2,2,3],[2,3,3],[3,4],[4]] => [[1,2,2,2,3,3,3],[3,4],[4]] => 5
[[1,2,2,2],[2,3,4],[3,4],[4]] => [[1,2,2,2,2,3,4],[3,4],[4]] => 5
[[1,2,2,3],[2,3,4],[3,4],[4]] => [[1,2,2,2,3,3,4],[3,4],[4]] => 5
[[1,2,2,4],[2,3,4],[3,4],[4]] => [[1,2,2,2,3,4,4],[3,4],[4]] => 5
[[1,2,3,3],[2,3,4],[3,4],[4]] => [[1,2,2,3,3,3,4],[3,4],[4]] => 5
[[1,2,3,4],[2,3,4],[3,4],[4]] => [[1,2,2,3,3,4,4],[3,4],[4]] => 5
[[2]] => [[2]] => 2
[[1,1]] => [[1,1]] => 1
[[3]] => [[3]] => 3
[[1,1,1]] => [[1,1,1]] => 1
[[4]] => [[4]] => 4
[[1,1,1,1]] => [[1,1,1,1]] => 1
[[5]] => [[5]] => 5
[[1,1,1,1,1]] => [[1,1,1,1,1]] => 1
[[6]] => [[6]] => 6
[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 1
[[1,2,3,4,5],[6]] => [[1,2,3,4,5,6]] => 1
[[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => 1
[[1,2,3,4],[5],[6]] => [[1,2,3,4,5],[6]] => 1
[[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,5],[4,6]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,5],[4],[6]] => [[1,2,3,4,6],[5]] => 1
[[1,2,3,4],[5,6]] => [[1,2,3,4,5,6]] => 1
[[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => 1
[[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => 1
[[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => 1
[[1,2,4,5],[3,6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => 7
[[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => 7
[[1,2,4,5],[3],[6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => 1
[[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => 1
[[1,2,3,6],[4,5]] => [[1,2,3,4,5],[6]] => 1
[[1,2,3],[4,5],[6]] => [[1,2,3,4,5],[6]] => 1
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => 1
[[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => 1
[[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => 1
[[1,2,3],[4,6],[5]] => [[1,2,3,4,6],[5]] => 1
[[1,2,4],[3,6],[5]] => [[1,2,3,5,6],[4]] => 1
[[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => 1
[[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => 1
[[1,3,4,5,6],[2]] => [[1,2,4,5,6],[3]] => 1
[[1,3,4,5],[2,6]] => [[1,2,4,5,6],[3]] => 1
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => 7
[[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => 7
[[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => 6
[[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => 6
[[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => 6
[[1,3,4],[2,5,6]] => [[1,2,4,5,6],[3]] => 1
[[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => 6
[[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => 6
[[1,3,4,5],[2],[6]] => [[1,2,4,5,6],[3]] => 1
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 1
[[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => 1
[[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => 1
[[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => 1
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => 1
[[1,3,4],[2,6],[5]] => [[1,2,4,5,6],[3]] => 1
[[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => 1
[[1,3],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6]] => 1
[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]] => 7
[[1,2,5],[3,4,6]] => [[1,2,3,4,6],[5]] => 1
[[1,2,5],[3,4],[6]] => [[1,2,3,4],[5,6]] => 7
[[1,2,4],[3,5,6]] => [[1,2,3,5,6],[4]] => 1
[[1,2,6],[3,4],[5]] => [[1,2,3,4],[5],[6]] => 1
[[1,2],[3,4],[5],[6]] => [[1,2,3,4],[5],[6]] => 1
[[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => 1
[[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => 1
[[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => 7
[[1,4],[2,5],[3,6]] => [[1,2,5],[3,6],[4]] => 7
[[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => 7
[[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => 1
[[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => 1
[[1,4],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6]] => 1
[[1,2,3],[4,5,6]] => [[1,2,3,4,5,6]] => 1
[[1,2,6],[3,5],[4]] => [[1,2,3,5],[4],[6]] => 1
[[1,2],[3,5],[4],[6]] => [[1,2,3,5],[4],[6]] => 1
[[1,3,6],[2,5],[4]] => [[1,2,4,5],[3],[6]] => 1
[[1,3],[2,5],[4,6]] => [[1,2,4,5],[3,6]] => 7
[[1,3],[2,5],[4],[6]] => [[1,2,4,5],[3],[6]] => 1
[[1,2],[3,5],[4,6]] => [[1,2,3,5],[4,6]] => 7
[[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => 1
[[1,5],[2,6],[3],[4]] => [[1,2,6],[3],[4],[5]] => 1
[[1,5],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5]] => 1
[[1,2],[3,6],[4],[5]] => [[1,2,3,6],[4],[5]] => 1
[[1,3],[2,4],[5,6]] => [[1,2,4,6],[3,5]] => 6
[[1,3],[2,6],[4],[5]] => [[1,2,4,6],[3],[5]] => 1
[[1,2],[3,4],[5,6]] => [[1,2,3,4],[5,6]] => 7
[[1,4],[2,6],[3],[5]] => [[1,2,5,6],[3],[4]] => 1
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => 1
[[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => 1
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
The trace of a semistandard tableau.
This is the sum of the entries on the diagonal.
Map
catabolism
Description
Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).