Identifier
Identifier
Mp00071: Permutations descent compositionInteger compositions
Images
[1] => [1]
[1,2] => [2]
[2,1] => [1,1]
[1,2,3] => [3]
[1,3,2] => [2,1]
[2,1,3] => [1,2]
[2,3,1] => [2,1]
[3,1,2] => [1,2]
[3,2,1] => [1,1,1]
[1,2,3,4] => [4]
[1,2,4,3] => [3,1]
[1,3,2,4] => [2,2]
[1,3,4,2] => [3,1]
[1,4,2,3] => [2,2]
[1,4,3,2] => [2,1,1]
[2,1,3,4] => [1,3]
[2,1,4,3] => [1,2,1]
[2,3,1,4] => [2,2]
[2,3,4,1] => [3,1]
[2,4,1,3] => [2,2]
[2,4,3,1] => [2,1,1]
[3,1,2,4] => [1,3]
[3,1,4,2] => [1,2,1]
[3,2,1,4] => [1,1,2]
[3,2,4,1] => [1,2,1]
[3,4,1,2] => [2,2]
[3,4,2,1] => [2,1,1]
[4,1,2,3] => [1,3]
[4,1,3,2] => [1,2,1]
[4,2,1,3] => [1,1,2]
[4,2,3,1] => [1,2,1]
[4,3,1,2] => [1,1,2]
[4,3,2,1] => [1,1,1,1]
[1,2,3,4,5] => [5]
[1,2,3,5,4] => [4,1]
[1,2,4,3,5] => [3,2]
[1,2,4,5,3] => [4,1]
[1,2,5,3,4] => [3,2]
[1,2,5,4,3] => [3,1,1]
[1,3,2,4,5] => [2,3]
[1,3,2,5,4] => [2,2,1]
[1,3,4,2,5] => [3,2]
[1,3,4,5,2] => [4,1]
[1,3,5,2,4] => [3,2]
[1,3,5,4,2] => [3,1,1]
[1,4,2,3,5] => [2,3]
[1,4,2,5,3] => [2,2,1]
[1,4,3,2,5] => [2,1,2]
[1,4,3,5,2] => [2,2,1]
[1,4,5,2,3] => [3,2]
[1,4,5,3,2] => [3,1,1]
[1,5,2,3,4] => [2,3]
[1,5,2,4,3] => [2,2,1]
[1,5,3,2,4] => [2,1,2]
[1,5,3,4,2] => [2,2,1]
[1,5,4,2,3] => [2,1,2]
[1,5,4,3,2] => [2,1,1,1]
[2,1,3,4,5] => [1,4]
[2,1,3,5,4] => [1,3,1]
[2,1,4,3,5] => [1,2,2]
[2,1,4,5,3] => [1,3,1]
[2,1,5,3,4] => [1,2,2]
[2,1,5,4,3] => [1,2,1,1]
[2,3,1,4,5] => [2,3]
[2,3,1,5,4] => [2,2,1]
[2,3,4,1,5] => [3,2]
[2,3,4,5,1] => [4,1]
[2,3,5,1,4] => [3,2]
[2,3,5,4,1] => [3,1,1]
[2,4,1,3,5] => [2,3]
[2,4,1,5,3] => [2,2,1]
[2,4,3,1,5] => [2,1,2]
[2,4,3,5,1] => [2,2,1]
[2,4,5,1,3] => [3,2]
[2,4,5,3,1] => [3,1,1]
[2,5,1,3,4] => [2,3]
[2,5,1,4,3] => [2,2,1]
[2,5,3,1,4] => [2,1,2]
[2,5,3,4,1] => [2,2,1]
[2,5,4,1,3] => [2,1,2]
[2,5,4,3,1] => [2,1,1,1]
[3,1,2,4,5] => [1,4]
[3,1,2,5,4] => [1,3,1]
[3,1,4,2,5] => [1,2,2]
[3,1,4,5,2] => [1,3,1]
[3,1,5,2,4] => [1,2,2]
[3,1,5,4,2] => [1,2,1,1]
[3,2,1,4,5] => [1,1,3]
[3,2,1,5,4] => [1,1,2,1]
[3,2,4,1,5] => [1,2,2]
[3,2,4,5,1] => [1,3,1]
[3,2,5,1,4] => [1,2,2]
[3,2,5,4,1] => [1,2,1,1]
[3,4,1,2,5] => [2,3]
[3,4,1,5,2] => [2,2,1]
[3,4,2,1,5] => [2,1,2]
[3,4,2,5,1] => [2,2,1]
[3,4,5,1,2] => [3,2]
[3,4,5,2,1] => [3,1,1]
[3,5,1,2,4] => [2,3]
[3,5,1,4,2] => [2,2,1]
[3,5,2,1,4] => [2,1,2]
[3,5,2,4,1] => [2,2,1]
[3,5,4,1,2] => [2,1,2]
[3,5,4,2,1] => [2,1,1,1]
[4,1,2,3,5] => [1,4]
[4,1,2,5,3] => [1,3,1]
[4,1,3,2,5] => [1,2,2]
[4,1,3,5,2] => [1,3,1]
[4,1,5,2,3] => [1,2,2]
[4,1,5,3,2] => [1,2,1,1]
[4,2,1,3,5] => [1,1,3]
[4,2,1,5,3] => [1,1,2,1]
[4,2,3,1,5] => [1,2,2]
[4,2,3,5,1] => [1,3,1]
[4,2,5,1,3] => [1,2,2]
[4,2,5,3,1] => [1,2,1,1]
[4,3,1,2,5] => [1,1,3]
[4,3,1,5,2] => [1,1,2,1]
[4,3,2,1,5] => [1,1,1,2]
[4,3,2,5,1] => [1,1,2,1]
[4,3,5,1,2] => [1,2,2]
[4,3,5,2,1] => [1,2,1,1]
[4,5,1,2,3] => [2,3]
[4,5,1,3,2] => [2,2,1]
[4,5,2,1,3] => [2,1,2]
[4,5,2,3,1] => [2,2,1]
[4,5,3,1,2] => [2,1,2]
[4,5,3,2,1] => [2,1,1,1]
[5,1,2,3,4] => [1,4]
[5,1,2,4,3] => [1,3,1]
[5,1,3,2,4] => [1,2,2]
[5,1,3,4,2] => [1,3,1]
[5,1,4,2,3] => [1,2,2]
[5,1,4,3,2] => [1,2,1,1]
[5,2,1,3,4] => [1,1,3]
[5,2,1,4,3] => [1,1,2,1]
[5,2,3,1,4] => [1,2,2]
[5,2,3,4,1] => [1,3,1]
[5,2,4,1,3] => [1,2,2]
[5,2,4,3,1] => [1,2,1,1]
[5,3,1,2,4] => [1,1,3]
[5,3,1,4,2] => [1,1,2,1]
[5,3,2,1,4] => [1,1,1,2]
[5,3,2,4,1] => [1,1,2,1]
[5,3,4,1,2] => [1,2,2]
[5,3,4,2,1] => [1,2,1,1]
[5,4,1,2,3] => [1,1,3]
[5,4,1,3,2] => [1,1,2,1]
[5,4,2,1,3] => [1,1,1,2]
[5,4,2,3,1] => [1,1,2,1]
[5,4,3,1,2] => [1,1,1,2]
[5,4,3,2,1] => [1,1,1,1,1]
[1,2,3,4,5,6] => [6]
[1,2,3,4,6,5] => [5,1]
[1,2,3,5,4,6] => [4,2]
[1,2,3,5,6,4] => [5,1]
[1,2,3,6,4,5] => [4,2]
[1,2,3,6,5,4] => [4,1,1]
[1,2,4,3,5,6] => [3,3]
[1,2,4,3,6,5] => [3,2,1]
[1,2,4,5,3,6] => [4,2]
[1,2,4,5,6,3] => [5,1]
[1,2,4,6,3,5] => [4,2]
[1,2,4,6,5,3] => [4,1,1]
[1,2,5,3,4,6] => [3,3]
[1,2,5,3,6,4] => [3,2,1]
[1,2,5,4,3,6] => [3,1,2]
[1,2,5,4,6,3] => [3,2,1]
[1,2,5,6,3,4] => [4,2]
[1,2,5,6,4,3] => [4,1,1]
[1,2,6,3,4,5] => [3,3]
[1,2,6,3,5,4] => [3,2,1]
[1,2,6,4,3,5] => [3,1,2]
[1,2,6,4,5,3] => [3,2,1]
[1,2,6,5,3,4] => [3,1,2]
[1,2,6,5,4,3] => [3,1,1,1]
[1,3,2,4,5,6] => [2,4]
[1,3,2,4,6,5] => [2,3,1]
[1,3,2,5,4,6] => [2,2,2]
[1,3,2,5,6,4] => [2,3,1]
[1,3,2,6,4,5] => [2,2,2]
[1,3,2,6,5,4] => [2,2,1,1]
[1,3,4,2,5,6] => [3,3]
[1,3,4,2,6,5] => [3,2,1]
[1,3,4,5,2,6] => [4,2]
[1,3,4,5,6,2] => [5,1]
[1,3,4,6,2,5] => [4,2]
[1,3,4,6,5,2] => [4,1,1]
[1,3,5,2,4,6] => [3,3]
[1,3,5,2,6,4] => [3,2,1]
[1,3,5,4,2,6] => [3,1,2]
[1,3,5,4,6,2] => [3,2,1]
[1,3,5,6,2,4] => [4,2]
[1,3,5,6,4,2] => [4,1,1]
[1,3,6,2,4,5] => [3,3]
[1,3,6,2,5,4] => [3,2,1]
[1,3,6,4,2,5] => [3,1,2]
[1,3,6,4,5,2] => [3,2,1]
[1,3,6,5,2,4] => [3,1,2]
[1,3,6,5,4,2] => [3,1,1,1]
[1,4,2,3,5,6] => [2,4]
[1,4,2,3,6,5] => [2,3,1]
[1,4,2,5,3,6] => [2,2,2]
[1,4,2,5,6,3] => [2,3,1]
[1,4,2,6,3,5] => [2,2,2]
[1,4,2,6,5,3] => [2,2,1,1]
[1,4,3,2,5,6] => [2,1,3]
[1,4,3,2,6,5] => [2,1,2,1]
[1,4,3,5,2,6] => [2,2,2]
[1,4,3,5,6,2] => [2,3,1]
[1,4,3,6,2,5] => [2,2,2]
[1,4,3,6,5,2] => [2,2,1,1]
[1,4,5,2,3,6] => [3,3]
[1,4,5,2,6,3] => [3,2,1]
[1,4,5,3,2,6] => [3,1,2]
[1,4,5,3,6,2] => [3,2,1]
[1,4,5,6,2,3] => [4,2]
[1,4,5,6,3,2] => [4,1,1]
[1,4,6,2,3,5] => [3,3]
[1,4,6,2,5,3] => [3,2,1]
[1,4,6,3,2,5] => [3,1,2]
[1,4,6,3,5,2] => [3,2,1]
[1,4,6,5,2,3] => [3,1,2]
[1,4,6,5,3,2] => [3,1,1,1]
[1,5,2,3,4,6] => [2,4]
[1,5,2,3,6,4] => [2,3,1]
[1,5,2,4,3,6] => [2,2,2]
[1,5,2,4,6,3] => [2,3,1]
[1,5,2,6,3,4] => [2,2,2]
[1,5,2,6,4,3] => [2,2,1,1]
[1,5,3,2,4,6] => [2,1,3]
[1,5,3,2,6,4] => [2,1,2,1]
[1,5,3,4,2,6] => [2,2,2]
[1,5,3,4,6,2] => [2,3,1]
[1,5,3,6,2,4] => [2,2,2]
[1,5,3,6,4,2] => [2,2,1,1]
[1,5,4,2,3,6] => [2,1,3]
[1,5,4,2,6,3] => [2,1,2,1]
[1,5,4,3,2,6] => [2,1,1,2]
[1,5,4,3,6,2] => [2,1,2,1]
[1,5,4,6,2,3] => [2,2,2]
[1,5,4,6,3,2] => [2,2,1,1]
[1,5,6,2,3,4] => [3,3]
[1,5,6,2,4,3] => [3,2,1]
[1,5,6,3,2,4] => [3,1,2]
[1,5,6,3,4,2] => [3,2,1]
[1,5,6,4,2,3] => [3,1,2]
[1,5,6,4,3,2] => [3,1,1,1]
[1,6,2,3,4,5] => [2,4]
[1,6,2,3,5,4] => [2,3,1]
[1,6,2,4,3,5] => [2,2,2]
[1,6,2,4,5,3] => [2,3,1]
[1,6,2,5,3,4] => [2,2,2]
[1,6,2,5,4,3] => [2,2,1,1]
[1,6,3,2,4,5] => [2,1,3]
[1,6,3,2,5,4] => [2,1,2,1]
[1,6,3,4,2,5] => [2,2,2]
[1,6,3,4,5,2] => [2,3,1]
[1,6,3,5,2,4] => [2,2,2]
[1,6,3,5,4,2] => [2,2,1,1]
[1,6,4,2,3,5] => [2,1,3]
[1,6,4,2,5,3] => [2,1,2,1]
[1,6,4,3,2,5] => [2,1,1,2]
[1,6,4,3,5,2] => [2,1,2,1]
[1,6,4,5,2,3] => [2,2,2]
[1,6,4,5,3,2] => [2,2,1,1]
[1,6,5,2,3,4] => [2,1,3]
[1,6,5,2,4,3] => [2,1,2,1]
[1,6,5,3,2,4] => [2,1,1,2]
[1,6,5,3,4,2] => [2,1,2,1]
[1,6,5,4,2,3] => [2,1,1,2]
[1,6,5,4,3,2] => [2,1,1,1,1]
[2,1,3,4,5,6] => [1,5]
[2,1,3,4,6,5] => [1,4,1]
[2,1,3,5,4,6] => [1,3,2]
[2,1,3,5,6,4] => [1,4,1]
[2,1,3,6,4,5] => [1,3,2]
[2,1,3,6,5,4] => [1,3,1,1]
[2,1,4,3,5,6] => [1,2,3]
[2,1,4,3,6,5] => [1,2,2,1]
[2,1,4,5,3,6] => [1,3,2]
[2,1,4,5,6,3] => [1,4,1]
[2,1,4,6,3,5] => [1,3,2]
[2,1,4,6,5,3] => [1,3,1,1]
[2,1,5,3,4,6] => [1,2,3]
[2,1,5,3,6,4] => [1,2,2,1]
[2,1,5,4,3,6] => [1,2,1,2]
[2,1,5,4,6,3] => [1,2,2,1]
[2,1,5,6,3,4] => [1,3,2]
[2,1,5,6,4,3] => [1,3,1,1]
[2,1,6,3,4,5] => [1,2,3]
[2,1,6,3,5,4] => [1,2,2,1]
[2,1,6,4,3,5] => [1,2,1,2]
[2,1,6,4,5,3] => [1,2,2,1]
[2,1,6,5,3,4] => [1,2,1,2]
[2,1,6,5,4,3] => [1,2,1,1,1]
[2,3,1,4,5,6] => [2,4]
[2,3,1,4,6,5] => [2,3,1]
[2,3,1,5,4,6] => [2,2,2]
[2,3,1,5,6,4] => [2,3,1]
[2,3,1,6,4,5] => [2,2,2]
[2,3,1,6,5,4] => [2,2,1,1]
[2,3,4,1,5,6] => [3,3]
[2,3,4,1,6,5] => [3,2,1]
[2,3,4,5,1,6] => [4,2]
[2,3,4,5,6,1] => [5,1]
[2,3,4,6,1,5] => [4,2]
[2,3,4,6,5,1] => [4,1,1]
[2,3,5,1,4,6] => [3,3]
[2,3,5,1,6,4] => [3,2,1]
[2,3,5,4,1,6] => [3,1,2]
[2,3,5,4,6,1] => [3,2,1]
[2,3,5,6,1,4] => [4,2]
[2,3,5,6,4,1] => [4,1,1]
[2,3,6,1,4,5] => [3,3]
[2,3,6,1,5,4] => [3,2,1]
[2,3,6,4,1,5] => [3,1,2]
[2,3,6,4,5,1] => [3,2,1]
[2,3,6,5,1,4] => [3,1,2]
[2,3,6,5,4,1] => [3,1,1,1]
[2,4,1,3,5,6] => [2,4]
[2,4,1,3,6,5] => [2,3,1]
[2,4,1,5,3,6] => [2,2,2]
[2,4,1,5,6,3] => [2,3,1]
[2,4,1,6,3,5] => [2,2,2]
[2,4,1,6,5,3] => [2,2,1,1]
[2,4,3,1,5,6] => [2,1,3]
[2,4,3,1,6,5] => [2,1,2,1]
[2,4,3,5,1,6] => [2,2,2]
[2,4,3,5,6,1] => [2,3,1]
[2,4,3,6,1,5] => [2,2,2]
[2,4,3,6,5,1] => [2,2,1,1]
[2,4,5,1,3,6] => [3,3]
[2,4,5,1,6,3] => [3,2,1]
[2,4,5,3,1,6] => [3,1,2]
[2,4,5,3,6,1] => [3,2,1]
[2,4,5,6,1,3] => [4,2]
[2,4,5,6,3,1] => [4,1,1]
[2,4,6,1,3,5] => [3,3]
[2,4,6,1,5,3] => [3,2,1]
[2,4,6,3,1,5] => [3,1,2]
[2,4,6,3,5,1] => [3,2,1]
[2,4,6,5,1,3] => [3,1,2]
[2,4,6,5,3,1] => [3,1,1,1]
[2,5,1,3,4,6] => [2,4]
[2,5,1,3,6,4] => [2,3,1]
[2,5,1,4,3,6] => [2,2,2]
[2,5,1,4,6,3] => [2,3,1]
[2,5,1,6,3,4] => [2,2,2]
[2,5,1,6,4,3] => [2,2,1,1]
[2,5,3,1,4,6] => [2,1,3]
[2,5,3,1,6,4] => [2,1,2,1]
[2,5,3,4,1,6] => [2,2,2]
[2,5,3,4,6,1] => [2,3,1]
[2,5,3,6,1,4] => [2,2,2]
[2,5,3,6,4,1] => [2,2,1,1]
[2,5,4,1,3,6] => [2,1,3]
[2,5,4,1,6,3] => [2,1,2,1]
[2,5,4,3,1,6] => [2,1,1,2]
[2,5,4,3,6,1] => [2,1,2,1]
[2,5,4,6,1,3] => [2,2,2]
[2,5,4,6,3,1] => [2,2,1,1]
[2,5,6,1,3,4] => [3,3]
[2,5,6,1,4,3] => [3,2,1]
[2,5,6,3,1,4] => [3,1,2]
[2,5,6,3,4,1] => [3,2,1]
[2,5,6,4,1,3] => [3,1,2]
[2,5,6,4,3,1] => [3,1,1,1]
[2,6,1,3,4,5] => [2,4]
[2,6,1,3,5,4] => [2,3,1]
[2,6,1,4,3,5] => [2,2,2]
[2,6,1,4,5,3] => [2,3,1]
[2,6,1,5,3,4] => [2,2,2]
[2,6,1,5,4,3] => [2,2,1,1]
[2,6,3,1,4,5] => [2,1,3]
[2,6,3,1,5,4] => [2,1,2,1]
[2,6,3,4,1,5] => [2,2,2]
[2,6,3,4,5,1] => [2,3,1]
[2,6,3,5,1,4] => [2,2,2]
[2,6,3,5,4,1] => [2,2,1,1]
[2,6,4,1,3,5] => [2,1,3]
[2,6,4,1,5,3] => [2,1,2,1]
[2,6,4,3,1,5] => [2,1,1,2]
[2,6,4,3,5,1] => [2,1,2,1]
[2,6,4,5,1,3] => [2,2,2]
[2,6,4,5,3,1] => [2,2,1,1]
[2,6,5,1,3,4] => [2,1,3]
[2,6,5,1,4,3] => [2,1,2,1]
[2,6,5,3,1,4] => [2,1,1,2]
[2,6,5,3,4,1] => [2,1,2,1]
[2,6,5,4,1,3] => [2,1,1,2]
[2,6,5,4,3,1] => [2,1,1,1,1]
[3,1,2,4,5,6] => [1,5]
[3,1,2,4,6,5] => [1,4,1]
[3,1,2,5,4,6] => [1,3,2]
[3,1,2,5,6,4] => [1,4,1]
[3,1,2,6,4,5] => [1,3,2]
[3,1,2,6,5,4] => [1,3,1,1]
[3,1,4,2,5,6] => [1,2,3]
[3,1,4,2,6,5] => [1,2,2,1]
[3,1,4,5,2,6] => [1,3,2]
[3,1,4,5,6,2] => [1,4,1]
[3,1,4,6,2,5] => [1,3,2]
[3,1,4,6,5,2] => [1,3,1,1]
[3,1,5,2,4,6] => [1,2,3]
[3,1,5,2,6,4] => [1,2,2,1]
[3,1,5,4,2,6] => [1,2,1,2]
[3,1,5,4,6,2] => [1,2,2,1]
[3,1,5,6,2,4] => [1,3,2]
[3,1,5,6,4,2] => [1,3,1,1]
[3,1,6,2,4,5] => [1,2,3]
[3,1,6,2,5,4] => [1,2,2,1]
[3,1,6,4,2,5] => [1,2,1,2]
[3,1,6,4,5,2] => [1,2,2,1]
[3,1,6,5,2,4] => [1,2,1,2]
[3,1,6,5,4,2] => [1,2,1,1,1]
[3,2,1,4,5,6] => [1,1,4]
[3,2,1,4,6,5] => [1,1,3,1]
[3,2,1,5,4,6] => [1,1,2,2]
[3,2,1,5,6,4] => [1,1,3,1]
[3,2,1,6,4,5] => [1,1,2,2]
[3,2,1,6,5,4] => [1,1,2,1,1]
[3,2,4,1,5,6] => [1,2,3]
[3,2,4,1,6,5] => [1,2,2,1]
[3,2,4,5,1,6] => [1,3,2]
[3,2,4,5,6,1] => [1,4,1]
[3,2,4,6,1,5] => [1,3,2]
[3,2,4,6,5,1] => [1,3,1,1]
[3,2,5,1,4,6] => [1,2,3]
[3,2,5,1,6,4] => [1,2,2,1]
[3,2,5,4,1,6] => [1,2,1,2]
[3,2,5,4,6,1] => [1,2,2,1]
[3,2,5,6,1,4] => [1,3,2]
[3,2,5,6,4,1] => [1,3,1,1]
[3,2,6,1,4,5] => [1,2,3]
[3,2,6,1,5,4] => [1,2,2,1]
[3,2,6,4,1,5] => [1,2,1,2]
[3,2,6,4,5,1] => [1,2,2,1]
[3,2,6,5,1,4] => [1,2,1,2]
[3,2,6,5,4,1] => [1,2,1,1,1]
[3,4,1,2,5,6] => [2,4]
[3,4,1,2,6,5] => [2,3,1]
[3,4,1,5,2,6] => [2,2,2]
[3,4,1,5,6,2] => [2,3,1]
[3,4,1,6,2,5] => [2,2,2]
[3,4,1,6,5,2] => [2,2,1,1]
[3,4,2,1,5,6] => [2,1,3]
[3,4,2,1,6,5] => [2,1,2,1]
[3,4,2,5,1,6] => [2,2,2]
[3,4,2,5,6,1] => [2,3,1]
[3,4,2,6,1,5] => [2,2,2]
[3,4,2,6,5,1] => [2,2,1,1]
[3,4,5,1,2,6] => [3,3]
[3,4,5,1,6,2] => [3,2,1]
[3,4,5,2,1,6] => [3,1,2]
[3,4,5,2,6,1] => [3,2,1]
[3,4,5,6,1,2] => [4,2]
[3,4,5,6,2,1] => [4,1,1]
[3,4,6,1,2,5] => [3,3]
[3,4,6,1,5,2] => [3,2,1]
[3,4,6,2,1,5] => [3,1,2]
[3,4,6,2,5,1] => [3,2,1]
[3,4,6,5,1,2] => [3,1,2]
[3,4,6,5,2,1] => [3,1,1,1]
[3,5,1,2,4,6] => [2,4]
[3,5,1,2,6,4] => [2,3,1]
[3,5,1,4,2,6] => [2,2,2]
[3,5,1,4,6,2] => [2,3,1]
[3,5,1,6,2,4] => [2,2,2]
[3,5,1,6,4,2] => [2,2,1,1]
[3,5,2,1,4,6] => [2,1,3]
[3,5,2,1,6,4] => [2,1,2,1]
[3,5,2,4,1,6] => [2,2,2]
[3,5,2,4,6,1] => [2,3,1]
[3,5,2,6,1,4] => [2,2,2]
[3,5,2,6,4,1] => [2,2,1,1]
[3,5,4,1,2,6] => [2,1,3]
[3,5,4,1,6,2] => [2,1,2,1]
[3,5,4,2,1,6] => [2,1,1,2]
[3,5,4,2,6,1] => [2,1,2,1]
[3,5,4,6,1,2] => [2,2,2]
[3,5,4,6,2,1] => [2,2,1,1]
[3,5,6,1,2,4] => [3,3]
[3,5,6,1,4,2] => [3,2,1]
[3,5,6,2,1,4] => [3,1,2]
[3,5,6,2,4,1] => [3,2,1]
[3,5,6,4,1,2] => [3,1,2]
[3,5,6,4,2,1] => [3,1,1,1]
[3,6,1,2,4,5] => [2,4]
[3,6,1,2,5,4] => [2,3,1]
[3,6,1,4,2,5] => [2,2,2]
[3,6,1,4,5,2] => [2,3,1]
[3,6,1,5,2,4] => [2,2,2]
[3,6,1,5,4,2] => [2,2,1,1]
[3,6,2,1,4,5] => [2,1,3]
[3,6,2,1,5,4] => [2,1,2,1]
[3,6,2,4,1,5] => [2,2,2]
[3,6,2,4,5,1] => [2,3,1]
[3,6,2,5,1,4] => [2,2,2]
[3,6,2,5,4,1] => [2,2,1,1]
[3,6,4,1,2,5] => [2,1,3]
[3,6,4,1,5,2] => [2,1,2,1]
[3,6,4,2,1,5] => [2,1,1,2]
[3,6,4,2,5,1] => [2,1,2,1]
[3,6,4,5,1,2] => [2,2,2]
[3,6,4,5,2,1] => [2,2,1,1]
[3,6,5,1,2,4] => [2,1,3]
[3,6,5,1,4,2] => [2,1,2,1]
[3,6,5,2,1,4] => [2,1,1,2]
[3,6,5,2,4,1] => [2,1,2,1]
[3,6,5,4,1,2] => [2,1,1,2]
[3,6,5,4,2,1] => [2,1,1,1,1]
[4,1,2,3,5,6] => [1,5]
[4,1,2,3,6,5] => [1,4,1]
[4,1,2,5,3,6] => [1,3,2]
[4,1,2,5,6,3] => [1,4,1]
[4,1,2,6,3,5] => [1,3,2]
[4,1,2,6,5,3] => [1,3,1,1]
[4,1,3,2,5,6] => [1,2,3]
[4,1,3,2,6,5] => [1,2,2,1]
[4,1,3,5,2,6] => [1,3,2]
[4,1,3,5,6,2] => [1,4,1]
[4,1,3,6,2,5] => [1,3,2]
[4,1,3,6,5,2] => [1,3,1,1]
[4,1,5,2,3,6] => [1,2,3]
[4,1,5,2,6,3] => [1,2,2,1]
[4,1,5,3,2,6] => [1,2,1,2]
[4,1,5,3,6,2] => [1,2,2,1]
[4,1,5,6,2,3] => [1,3,2]
[4,1,5,6,3,2] => [1,3,1,1]
[4,1,6,2,3,5] => [1,2,3]
[4,1,6,2,5,3] => [1,2,2,1]
[4,1,6,3,2,5] => [1,2,1,2]
[4,1,6,3,5,2] => [1,2,2,1]
[4,1,6,5,2,3] => [1,2,1,2]
[4,1,6,5,3,2] => [1,2,1,1,1]
[4,2,1,3,5,6] => [1,1,4]
[4,2,1,3,6,5] => [1,1,3,1]
[4,2,1,5,3,6] => [1,1,2,2]
[4,2,1,5,6,3] => [1,1,3,1]
[4,2,1,6,3,5] => [1,1,2,2]
[4,2,1,6,5,3] => [1,1,2,1,1]
[4,2,3,1,5,6] => [1,2,3]
[4,2,3,1,6,5] => [1,2,2,1]
[4,2,3,5,1,6] => [1,3,2]
[4,2,3,5,6,1] => [1,4,1]
[4,2,3,6,1,5] => [1,3,2]
[4,2,3,6,5,1] => [1,3,1,1]
[4,2,5,1,3,6] => [1,2,3]
[4,2,5,1,6,3] => [1,2,2,1]
[4,2,5,3,1,6] => [1,2,1,2]
[4,2,5,3,6,1] => [1,2,2,1]
[4,2,5,6,1,3] => [1,3,2]
[4,2,5,6,3,1] => [1,3,1,1]
[4,2,6,1,3,5] => [1,2,3]
[4,2,6,1,5,3] => [1,2,2,1]
[4,2,6,3,1,5] => [1,2,1,2]
[4,2,6,3,5,1] => [1,2,2,1]
[4,2,6,5,1,3] => [1,2,1,2]
[4,2,6,5,3,1] => [1,2,1,1,1]
[4,3,1,2,5,6] => [1,1,4]
[4,3,1,2,6,5] => [1,1,3,1]
[4,3,1,5,2,6] => [1,1,2,2]
[4,3,1,5,6,2] => [1,1,3,1]
[4,3,1,6,2,5] => [1,1,2,2]
[4,3,1,6,5,2] => [1,1,2,1,1]
[4,3,2,1,5,6] => [1,1,1,3]
[4,3,2,1,6,5] => [1,1,1,2,1]
[4,3,2,5,1,6] => [1,1,2,2]
[4,3,2,5,6,1] => [1,1,3,1]
[4,3,2,6,1,5] => [1,1,2,2]
[4,3,2,6,5,1] => [1,1,2,1,1]
[4,3,5,1,2,6] => [1,2,3]
[4,3,5,1,6,2] => [1,2,2,1]
[4,3,5,2,1,6] => [1,2,1,2]
[4,3,5,2,6,1] => [1,2,2,1]
[4,3,5,6,1,2] => [1,3,2]
[4,3,5,6,2,1] => [1,3,1,1]
[4,3,6,1,2,5] => [1,2,3]
[4,3,6,1,5,2] => [1,2,2,1]
[4,3,6,2,1,5] => [1,2,1,2]
[4,3,6,2,5,1] => [1,2,2,1]
[4,3,6,5,1,2] => [1,2,1,2]
[4,3,6,5,2,1] => [1,2,1,1,1]
[4,5,1,2,3,6] => [2,4]
[4,5,1,2,6,3] => [2,3,1]
[4,5,1,3,2,6] => [2,2,2]
[4,5,1,3,6,2] => [2,3,1]
[4,5,1,6,2,3] => [2,2,2]
[4,5,1,6,3,2] => [2,2,1,1]
[4,5,2,1,3,6] => [2,1,3]
[4,5,2,1,6,3] => [2,1,2,1]
[4,5,2,3,1,6] => [2,2,2]
[4,5,2,3,6,1] => [2,3,1]
[4,5,2,6,1,3] => [2,2,2]
[4,5,2,6,3,1] => [2,2,1,1]
[4,5,3,1,2,6] => [2,1,3]
[4,5,3,1,6,2] => [2,1,2,1]
[4,5,3,2,1,6] => [2,1,1,2]
[4,5,3,2,6,1] => [2,1,2,1]
[4,5,3,6,1,2] => [2,2,2]
[4,5,3,6,2,1] => [2,2,1,1]
[4,5,6,1,2,3] => [3,3]
[4,5,6,1,3,2] => [3,2,1]
[4,5,6,2,1,3] => [3,1,2]
[4,5,6,2,3,1] => [3,2,1]
[4,5,6,3,1,2] => [3,1,2]
[4,5,6,3,2,1] => [3,1,1,1]
[4,6,1,2,3,5] => [2,4]
[4,6,1,2,5,3] => [2,3,1]
[4,6,1,3,2,5] => [2,2,2]
[4,6,1,3,5,2] => [2,3,1]
[4,6,1,5,2,3] => [2,2,2]
[4,6,1,5,3,2] => [2,2,1,1]
[4,6,2,1,3,5] => [2,1,3]
[4,6,2,1,5,3] => [2,1,2,1]
[4,6,2,3,1,5] => [2,2,2]
[4,6,2,3,5,1] => [2,3,1]
[4,6,2,5,1,3] => [2,2,2]
[4,6,2,5,3,1] => [2,2,1,1]
[4,6,3,1,2,5] => [2,1,3]
[4,6,3,1,5,2] => [2,1,2,1]
[4,6,3,2,1,5] => [2,1,1,2]
[4,6,3,2,5,1] => [2,1,2,1]
[4,6,3,5,1,2] => [2,2,2]
[4,6,3,5,2,1] => [2,2,1,1]
[4,6,5,1,2,3] => [2,1,3]
[4,6,5,1,3,2] => [2,1,2,1]
[4,6,5,2,1,3] => [2,1,1,2]
[4,6,5,2,3,1] => [2,1,2,1]
[4,6,5,3,1,2] => [2,1,1,2]
[4,6,5,3,2,1] => [2,1,1,1,1]
[5,1,2,3,4,6] => [1,5]
[5,1,2,3,6,4] => [1,4,1]
[5,1,2,4,3,6] => [1,3,2]
[5,1,2,4,6,3] => [1,4,1]
[5,1,2,6,3,4] => [1,3,2]
[5,1,2,6,4,3] => [1,3,1,1]
[5,1,3,2,4,6] => [1,2,3]
[5,1,3,2,6,4] => [1,2,2,1]
[5,1,3,4,2,6] => [1,3,2]
[5,1,3,4,6,2] => [1,4,1]
[5,1,3,6,2,4] => [1,3,2]
[5,1,3,6,4,2] => [1,3,1,1]
[5,1,4,2,3,6] => [1,2,3]
[5,1,4,2,6,3] => [1,2,2,1]
[5,1,4,3,2,6] => [1,2,1,2]
[5,1,4,3,6,2] => [1,2,2,1]
[5,1,4,6,2,3] => [1,3,2]
[5,1,4,6,3,2] => [1,3,1,1]
[5,1,6,2,3,4] => [1,2,3]
[5,1,6,2,4,3] => [1,2,2,1]
[5,1,6,3,2,4] => [1,2,1,2]
[5,1,6,3,4,2] => [1,2,2,1]
[5,1,6,4,2,3] => [1,2,1,2]
[5,1,6,4,3,2] => [1,2,1,1,1]
[5,2,1,3,4,6] => [1,1,4]
[5,2,1,3,6,4] => [1,1,3,1]
[5,2,1,4,3,6] => [1,1,2,2]
[5,2,1,4,6,3] => [1,1,3,1]
[5,2,1,6,3,4] => [1,1,2,2]
[5,2,1,6,4,3] => [1,1,2,1,1]
[5,2,3,1,4,6] => [1,2,3]
[5,2,3,1,6,4] => [1,2,2,1]
[5,2,3,4,1,6] => [1,3,2]
[5,2,3,4,6,1] => [1,4,1]
[5,2,3,6,1,4] => [1,3,2]
[5,2,3,6,4,1] => [1,3,1,1]
[5,2,4,1,3,6] => [1,2,3]
[5,2,4,1,6,3] => [1,2,2,1]
[5,2,4,3,1,6] => [1,2,1,2]
[5,2,4,3,6,1] => [1,2,2,1]
[5,2,4,6,1,3] => [1,3,2]
[5,2,4,6,3,1] => [1,3,1,1]
[5,2,6,1,3,4] => [1,2,3]
[5,2,6,1,4,3] => [1,2,2,1]
[5,2,6,3,1,4] => [1,2,1,2]
[5,2,6,3,4,1] => [1,2,2,1]
[5,2,6,4,1,3] => [1,2,1,2]
[5,2,6,4,3,1] => [1,2,1,1,1]
[5,3,1,2,4,6] => [1,1,4]
[5,3,1,2,6,4] => [1,1,3,1]
[5,3,1,4,2,6] => [1,1,2,2]
[5,3,1,4,6,2] => [1,1,3,1]
[5,3,1,6,2,4] => [1,1,2,2]
[5,3,1,6,4,2] => [1,1,2,1,1]
[5,3,2,1,4,6] => [1,1,1,3]
[5,3,2,1,6,4] => [1,1,1,2,1]
[5,3,2,4,1,6] => [1,1,2,2]
[5,3,2,4,6,1] => [1,1,3,1]
[5,3,2,6,1,4] => [1,1,2,2]
[5,3,2,6,4,1] => [1,1,2,1,1]
[5,3,4,1,2,6] => [1,2,3]
[5,3,4,1,6,2] => [1,2,2,1]
[5,3,4,2,1,6] => [1,2,1,2]
[5,3,4,2,6,1] => [1,2,2,1]
[5,3,4,6,1,2] => [1,3,2]
[5,3,4,6,2,1] => [1,3,1,1]
[5,3,6,1,2,4] => [1,2,3]
[5,3,6,1,4,2] => [1,2,2,1]
[5,3,6,2,1,4] => [1,2,1,2]
[5,3,6,2,4,1] => [1,2,2,1]
[5,3,6,4,1,2] => [1,2,1,2]
[5,3,6,4,2,1] => [1,2,1,1,1]
[5,4,1,2,3,6] => [1,1,4]
[5,4,1,2,6,3] => [1,1,3,1]
[5,4,1,3,2,6] => [1,1,2,2]
[5,4,1,3,6,2] => [1,1,3,1]
[5,4,1,6,2,3] => [1,1,2,2]
[5,4,1,6,3,2] => [1,1,2,1,1]
[5,4,2,1,3,6] => [1,1,1,3]
[5,4,2,1,6,3] => [1,1,1,2,1]
[5,4,2,3,1,6] => [1,1,2,2]
[5,4,2,3,6,1] => [1,1,3,1]
[5,4,2,6,1,3] => [1,1,2,2]
[5,4,2,6,3,1] => [1,1,2,1,1]
[5,4,3,1,2,6] => [1,1,1,3]
[5,4,3,1,6,2] => [1,1,1,2,1]
[5,4,3,2,1,6] => [1,1,1,1,2]
[5,4,3,2,6,1] => [1,1,1,2,1]
[5,4,3,6,1,2] => [1,1,2,2]
[5,4,3,6,2,1] => [1,1,2,1,1]
[5,4,6,1,2,3] => [1,2,3]
[5,4,6,1,3,2] => [1,2,2,1]
[5,4,6,2,1,3] => [1,2,1,2]
[5,4,6,2,3,1] => [1,2,2,1]
[5,4,6,3,1,2] => [1,2,1,2]
[5,4,6,3,2,1] => [1,2,1,1,1]
[5,6,1,2,3,4] => [2,4]
[5,6,1,2,4,3] => [2,3,1]
[5,6,1,3,2,4] => [2,2,2]
[5,6,1,3,4,2] => [2,3,1]
[5,6,1,4,2,3] => [2,2,2]
[5,6,1,4,3,2] => [2,2,1,1]
[5,6,2,1,3,4] => [2,1,3]
[5,6,2,1,4,3] => [2,1,2,1]
[5,6,2,3,1,4] => [2,2,2]
[5,6,2,3,4,1] => [2,3,1]
[5,6,2,4,1,3] => [2,2,2]
[5,6,2,4,3,1] => [2,2,1,1]
[5,6,3,1,2,4] => [2,1,3]
[5,6,3,1,4,2] => [2,1,2,1]
[5,6,3,2,1,4] => [2,1,1,2]
[5,6,3,2,4,1] => [2,1,2,1]
[5,6,3,4,1,2] => [2,2,2]
[5,6,3,4,2,1] => [2,2,1,1]
[5,6,4,1,2,3] => [2,1,3]
[5,6,4,1,3,2] => [2,1,2,1]
[5,6,4,2,1,3] => [2,1,1,2]
[5,6,4,2,3,1] => [2,1,2,1]
[5,6,4,3,1,2] => [2,1,1,2]
[5,6,4,3,2,1] => [2,1,1,1,1]
[6,1,2,3,4,5] => [1,5]
[6,1,2,3,5,4] => [1,4,1]
[6,1,2,4,3,5] => [1,3,2]
[6,1,2,4,5,3] => [1,4,1]
[6,1,2,5,3,4] => [1,3,2]
[6,1,2,5,4,3] => [1,3,1,1]
[6,1,3,2,4,5] => [1,2,3]
[6,1,3,2,5,4] => [1,2,2,1]
[6,1,3,4,2,5] => [1,3,2]
[6,1,3,4,5,2] => [1,4,1]
[6,1,3,5,2,4] => [1,3,2]
[6,1,3,5,4,2] => [1,3,1,1]
[6,1,4,2,3,5] => [1,2,3]
[6,1,4,2,5,3] => [1,2,2,1]
[6,1,4,3,2,5] => [1,2,1,2]
[6,1,4,3,5,2] => [1,2,2,1]
[6,1,4,5,2,3] => [1,3,2]
[6,1,4,5,3,2] => [1,3,1,1]
[6,1,5,2,3,4] => [1,2,3]
[6,1,5,2,4,3] => [1,2,2,1]
[6,1,5,3,2,4] => [1,2,1,2]
[6,1,5,3,4,2] => [1,2,2,1]
[6,1,5,4,2,3] => [1,2,1,2]
[6,1,5,4,3,2] => [1,2,1,1,1]
[6,2,1,3,4,5] => [1,1,4]
[6,2,1,3,5,4] => [1,1,3,1]
[6,2,1,4,3,5] => [1,1,2,2]
[6,2,1,4,5,3] => [1,1,3,1]
[6,2,1,5,3,4] => [1,1,2,2]
[6,2,1,5,4,3] => [1,1,2,1,1]
[6,2,3,1,4,5] => [1,2,3]
[6,2,3,1,5,4] => [1,2,2,1]
[6,2,3,4,1,5] => [1,3,2]
[6,2,3,4,5,1] => [1,4,1]
[6,2,3,5,1,4] => [1,3,2]
[6,2,3,5,4,1] => [1,3,1,1]
[6,2,4,1,3,5] => [1,2,3]
[6,2,4,1,5,3] => [1,2,2,1]
[6,2,4,3,1,5] => [1,2,1,2]
[6,2,4,3,5,1] => [1,2,2,1]
[6,2,4,5,1,3] => [1,3,2]
[6,2,4,5,3,1] => [1,3,1,1]
[6,2,5,1,3,4] => [1,2,3]
[6,2,5,1,4,3] => [1,2,2,1]
[6,2,5,3,1,4] => [1,2,1,2]
[6,2,5,3,4,1] => [1,2,2,1]
[6,2,5,4,1,3] => [1,2,1,2]
[6,2,5,4,3,1] => [1,2,1,1,1]
[6,3,1,2,4,5] => [1,1,4]
[6,3,1,2,5,4] => [1,1,3,1]
[6,3,1,4,2,5] => [1,1,2,2]
[6,3,1,4,5,2] => [1,1,3,1]
[6,3,1,5,2,4] => [1,1,2,2]
[6,3,1,5,4,2] => [1,1,2,1,1]
[6,3,2,1,4,5] => [1,1,1,3]
[6,3,2,1,5,4] => [1,1,1,2,1]
[6,3,2,4,1,5] => [1,1,2,2]
[6,3,2,4,5,1] => [1,1,3,1]
[6,3,2,5,1,4] => [1,1,2,2]
[6,3,2,5,4,1] => [1,1,2,1,1]
[6,3,4,1,2,5] => [1,2,3]
[6,3,4,1,5,2] => [1,2,2,1]
[6,3,4,2,1,5] => [1,2,1,2]
[6,3,4,2,5,1] => [1,2,2,1]
[6,3,4,5,1,2] => [1,3,2]
[6,3,4,5,2,1] => [1,3,1,1]
[6,3,5,1,2,4] => [1,2,3]
[6,3,5,1,4,2] => [1,2,2,1]
[6,3,5,2,1,4] => [1,2,1,2]
[6,3,5,2,4,1] => [1,2,2,1]
[6,3,5,4,1,2] => [1,2,1,2]
[6,3,5,4,2,1] => [1,2,1,1,1]
[6,4,1,2,3,5] => [1,1,4]
[6,4,1,2,5,3] => [1,1,3,1]
[6,4,1,3,2,5] => [1,1,2,2]
[6,4,1,3,5,2] => [1,1,3,1]
[6,4,1,5,2,3] => [1,1,2,2]
[6,4,1,5,3,2] => [1,1,2,1,1]
[6,4,2,1,3,5] => [1,1,1,3]
[6,4,2,1,5,3] => [1,1,1,2,1]
[6,4,2,3,1,5] => [1,1,2,2]
[6,4,2,3,5,1] => [1,1,3,1]
[6,4,2,5,1,3] => [1,1,2,2]
[6,4,2,5,3,1] => [1,1,2,1,1]
[6,4,3,1,2,5] => [1,1,1,3]
[6,4,3,1,5,2] => [1,1,1,2,1]
[6,4,3,2,1,5] => [1,1,1,1,2]
[6,4,3,2,5,1] => [1,1,1,2,1]
[6,4,3,5,1,2] => [1,1,2,2]
[6,4,3,5,2,1] => [1,1,2,1,1]
[6,4,5,1,2,3] => [1,2,3]
[6,4,5,1,3,2] => [1,2,2,1]
[6,4,5,2,1,3] => [1,2,1,2]
[6,4,5,2,3,1] => [1,2,2,1]
[6,4,5,3,1,2] => [1,2,1,2]
[6,4,5,3,2,1] => [1,2,1,1,1]
[6,5,1,2,3,4] => [1,1,4]
[6,5,1,2,4,3] => [1,1,3,1]
[6,5,1,3,2,4] => [1,1,2,2]
[6,5,1,3,4,2] => [1,1,3,1]
[6,5,1,4,2,3] => [1,1,2,2]
[6,5,1,4,3,2] => [1,1,2,1,1]
[6,5,2,1,3,4] => [1,1,1,3]
[6,5,2,1,4,3] => [1,1,1,2,1]
[6,5,2,3,1,4] => [1,1,2,2]
[6,5,2,3,4,1] => [1,1,3,1]
[6,5,2,4,1,3] => [1,1,2,2]
[6,5,2,4,3,1] => [1,1,2,1,1]
[6,5,3,1,2,4] => [1,1,1,3]
[6,5,3,1,4,2] => [1,1,1,2,1]
[6,5,3,2,1,4] => [1,1,1,1,2]
[6,5,3,2,4,1] => [1,1,1,2,1]
[6,5,3,4,1,2] => [1,1,2,2]
[6,5,3,4,2,1] => [1,1,2,1,1]
[6,5,4,1,2,3] => [1,1,1,3]
[6,5,4,1,3,2] => [1,1,1,2,1]
[6,5,4,2,1,3] => [1,1,1,1,2]
[6,5,4,2,3,1] => [1,1,1,2,1]
[6,5,4,3,1,2] => [1,1,1,1,2]
[6,5,4,3,2,1] => [1,1,1,1,1,1]
[1,2,3,4,5,6,7] => [7]
[1,2,3,4,5,7,6] => [6,1]
[1,2,3,4,6,5,7] => [5,2]
[1,2,3,4,6,7,5] => [6,1]
[1,2,3,4,7,5,6] => [5,2]
[1,2,3,4,7,6,5] => [5,1,1]
[1,2,3,5,4,6,7] => [4,3]
[1,2,3,5,4,7,6] => [4,2,1]
[1,2,3,5,6,4,7] => [5,2]
[1,2,3,5,6,7,4] => [6,1]
[1,2,3,5,7,4,6] => [5,2]
[1,2,3,5,7,6,4] => [5,1,1]
[1,2,3,6,4,5,7] => [4,3]
[1,2,3,6,4,7,5] => [4,2,1]
[1,2,3,6,5,4,7] => [4,1,2]
[1,2,3,6,5,7,4] => [4,2,1]
[1,2,3,6,7,4,5] => [5,2]
[1,2,3,6,7,5,4] => [5,1,1]
[1,2,3,7,4,5,6] => [4,3]
[1,2,3,7,4,6,5] => [4,2,1]
[1,2,3,7,5,4,6] => [4,1,2]
[1,2,3,7,5,6,4] => [4,2,1]
[1,2,3,7,6,4,5] => [4,1,2]
[1,2,3,7,6,5,4] => [4,1,1,1]
[1,2,4,3,5,6,7] => [3,4]
[1,2,4,3,5,7,6] => [3,3,1]
[1,2,4,3,6,5,7] => [3,2,2]
[1,2,4,3,6,7,5] => [3,3,1]
[1,2,4,3,7,5,6] => [3,2,2]
[1,2,4,3,7,6,5] => [3,2,1,1]
[1,2,4,5,3,6,7] => [4,3]
[1,2,4,5,3,7,6] => [4,2,1]
[1,2,4,5,6,3,7] => [5,2]
[1,2,4,5,6,7,3] => [6,1]
[1,2,4,5,7,3,6] => [5,2]
[1,2,4,5,7,6,3] => [5,1,1]
[1,2,4,6,3,5,7] => [4,3]
[1,2,4,6,3,7,5] => [4,2,1]
[1,2,4,6,5,3,7] => [4,1,2]
[1,2,4,6,5,7,3] => [4,2,1]
[1,2,4,6,7,3,5] => [5,2]
[1,2,4,6,7,5,3] => [5,1,1]
[1,2,4,7,3,5,6] => [4,3]
[1,2,4,7,3,6,5] => [4,2,1]
[1,2,4,7,5,3,6] => [4,1,2]
[1,2,4,7,5,6,3] => [4,2,1]
[1,2,4,7,6,3,5] => [4,1,2]
[1,2,4,7,6,5,3] => [4,1,1,1]
[1,2,5,3,4,6,7] => [3,4]
[1,2,5,3,4,7,6] => [3,3,1]
[1,2,5,3,6,4,7] => [3,2,2]
[1,2,5,3,6,7,4] => [3,3,1]
[1,2,5,3,7,4,6] => [3,2,2]
[1,2,5,3,7,6,4] => [3,2,1,1]
[1,2,5,4,3,6,7] => [3,1,3]
[1,2,5,4,3,7,6] => [3,1,2,1]
[1,2,5,4,6,3,7] => [3,2,2]
[1,2,5,4,6,7,3] => [3,3,1]
[1,2,5,4,7,3,6] => [3,2,2]
[1,2,5,4,7,6,3] => [3,2,1,1]
[1,2,5,6,3,4,7] => [4,3]
[1,2,5,6,3,7,4] => [4,2,1]
[1,2,5,6,4,3,7] => [4,1,2]
[1,2,5,6,4,7,3] => [4,2,1]
[1,2,5,6,7,3,4] => [5,2]
[1,2,5,6,7,4,3] => [5,1,1]
[1,2,5,7,3,4,6] => [4,3]
[1,2,5,7,3,6,4] => [4,2,1]
[1,2,5,7,4,3,6] => [4,1,2]
[1,2,5,7,4,6,3] => [4,2,1]
[1,2,5,7,6,3,4] => [4,1,2]
[1,2,5,7,6,4,3] => [4,1,1,1]
[1,2,6,3,4,5,7] => [3,4]
[1,2,6,3,4,7,5] => [3,3,1]
[1,2,6,3,5,4,7] => [3,2,2]
[1,2,6,3,5,7,4] => [3,3,1]
[1,2,6,3,7,4,5] => [3,2,2]
[1,2,6,3,7,5,4] => [3,2,1,1]
[1,2,6,4,3,5,7] => [3,1,3]
[1,2,6,4,3,7,5] => [3,1,2,1]
[1,2,6,4,5,3,7] => [3,2,2]
[1,2,6,4,5,7,3] => [3,3,1]
[1,2,6,4,7,3,5] => [3,2,2]
[1,2,6,4,7,5,3] => [3,2,1,1]
[1,2,6,5,3,4,7] => [3,1,3]
[1,2,6,5,3,7,4] => [3,1,2,1]
[1,2,6,5,4,3,7] => [3,1,1,2]
[1,2,6,5,4,7,3] => [3,1,2,1]
[1,2,6,5,7,3,4] => [3,2,2]
[1,2,6,5,7,4,3] => [3,2,1,1]
[1,2,6,7,3,4,5] => [4,3]
[1,2,6,7,3,5,4] => [4,2,1]
[1,2,6,7,4,3,5] => [4,1,2]
[1,2,6,7,4,5,3] => [4,2,1]
[1,2,6,7,5,3,4] => [4,1,2]
[1,2,6,7,5,4,3] => [4,1,1,1]
[1,2,7,3,4,5,6] => [3,4]
[1,2,7,3,4,6,5] => [3,3,1]
[1,2,7,3,5,4,6] => [3,2,2]
[1,2,7,3,5,6,4] => [3,3,1]
[1,2,7,3,6,4,5] => [3,2,2]
[1,2,7,3,6,5,4] => [3,2,1,1]
[1,2,7,4,3,5,6] => [3,1,3]
[1,2,7,4,3,6,5] => [3,1,2,1]
[1,2,7,4,5,3,6] => [3,2,2]
[1,2,7,4,5,6,3] => [3,3,1]
[1,2,7,4,6,3,5] => [3,2,2]
[1,2,7,4,6,5,3] => [3,2,1,1]
[1,2,7,5,3,4,6] => [3,1,3]
[1,2,7,5,3,6,4] => [3,1,2,1]
[1,2,7,5,4,3,6] => [3,1,1,2]
[1,2,7,5,4,6,3] => [3,1,2,1]
[1,2,7,5,6,3,4] => [3,2,2]
[1,2,7,5,6,4,3] => [3,2,1,1]
[1,2,7,6,3,4,5] => [3,1,3]
[1,2,7,6,3,5,4] => [3,1,2,1]
[1,2,7,6,4,3,5] => [3,1,1,2]
[1,2,7,6,4,5,3] => [3,1,2,1]
[1,2,7,6,5,3,4] => [3,1,1,2]
[1,2,7,6,5,4,3] => [3,1,1,1,1]
[1,3,2,4,5,6,7] => [2,5]
[1,3,2,4,5,7,6] => [2,4,1]
[1,3,2,4,6,5,7] => [2,3,2]
[1,3,2,4,6,7,5] => [2,4,1]
[1,3,2,4,7,5,6] => [2,3,2]
[1,3,2,4,7,6,5] => [2,3,1,1]
[1,3,2,5,4,6,7] => [2,2,3]
[1,3,2,5,4,7,6] => [2,2,2,1]
[1,3,2,5,6,4,7] => [2,3,2]
[1,3,2,5,6,7,4] => [2,4,1]
[1,3,2,5,7,4,6] => [2,3,2]
[1,3,2,5,7,6,4] => [2,3,1,1]
[1,3,2,6,4,5,7] => [2,2,3]
[1,3,2,6,4,7,5] => [2,2,2,1]
[1,3,2,6,5,4,7] => [2,2,1,2]
[1,3,2,6,5,7,4] => [2,2,2,1]
[1,3,2,6,7,4,5] => [2,3,2]
[1,3,2,6,7,5,4] => [2,3,1,1]
[1,3,2,7,4,5,6] => [2,2,3]
[1,3,2,7,4,6,5] => [2,2,2,1]
[1,3,2,7,5,4,6] => [2,2,1,2]
[1,3,2,7,5,6,4] => [2,2,2,1]
[1,3,2,7,6,4,5] => [2,2,1,2]
[1,3,2,7,6,5,4] => [2,2,1,1,1]
[1,3,4,2,5,6,7] => [3,4]
[1,3,4,2,5,7,6] => [3,3,1]
[1,3,4,2,6,5,7] => [3,2,2]
[1,3,4,2,6,7,5] => [3,3,1]
[1,3,4,2,7,5,6] => [3,2,2]
[1,3,4,2,7,6,5] => [3,2,1,1]
[1,3,4,5,2,6,7] => [4,3]
[1,3,4,5,2,7,6] => [4,2,1]
[1,3,4,5,6,2,7] => [5,2]
[1,3,4,5,6,7,2] => [6,1]
[1,3,4,5,7,2,6] => [5,2]
[1,3,4,5,7,6,2] => [5,1,1]
[1,3,4,6,2,5,7] => [4,3]
[1,3,4,6,2,7,5] => [4,2,1]
[1,3,4,6,5,2,7] => [4,1,2]
[1,3,4,6,5,7,2] => [4,2,1]
[1,3,4,6,7,2,5] => [5,2]
[1,3,4,6,7,5,2] => [5,1,1]
[1,3,4,7,2,5,6] => [4,3]
[1,3,4,7,2,6,5] => [4,2,1]
[1,3,4,7,5,2,6] => [4,1,2]
[1,3,4,7,5,6,2] => [4,2,1]
[1,3,4,7,6,2,5] => [4,1,2]
[1,3,4,7,6,5,2] => [4,1,1,1]
[1,3,5,2,4,6,7] => [3,4]
[1,3,5,2,4,7,6] => [3,3,1]
[1,3,5,2,6,4,7] => [3,2,2]
[1,3,5,2,6,7,4] => [3,3,1]
[1,3,5,2,7,4,6] => [3,2,2]
[1,3,5,2,7,6,4] => [3,2,1,1]
[1,3,5,4,2,6,7] => [3,1,3]
[1,3,5,4,2,7,6] => [3,1,2,1]
[1,3,5,4,6,2,7] => [3,2,2]
[1,3,5,4,6,7,2] => [3,3,1]
[1,3,5,4,7,2,6] => [3,2,2]
[1,3,5,4,7,6,2] => [3,2,1,1]
[1,3,5,6,2,4,7] => [4,3]
[1,3,5,6,2,7,4] => [4,2,1]
[1,3,5,6,4,2,7] => [4,1,2]
[1,3,5,6,4,7,2] => [4,2,1]
[1,3,5,6,7,2,4] => [5,2]
[1,3,5,6,7,4,2] => [5,1,1]
[1,3,5,7,2,4,6] => [4,3]
[1,3,5,7,2,6,4] => [4,2,1]
[1,3,5,7,4,2,6] => [4,1,2]
[1,3,5,7,4,6,2] => [4,2,1]
[1,3,5,7,6,2,4] => [4,1,2]
[1,3,5,7,6,4,2] => [4,1,1,1]
[1,3,6,2,4,5,7] => [3,4]
[1,3,6,2,4,7,5] => [3,3,1]
[1,3,6,2,5,4,7] => [3,2,2]
[1,3,6,2,5,7,4] => [3,3,1]
[1,3,6,2,7,4,5] => [3,2,2]
[1,3,6,2,7,5,4] => [3,2,1,1]
[1,3,6,4,2,5,7] => [3,1,3]
[1,3,6,4,2,7,5] => [3,1,2,1]
[1,3,6,4,5,2,7] => [3,2,2]
[1,3,6,4,5,7,2] => [3,3,1]
[1,3,6,4,7,2,5] => [3,2,2]
[1,3,6,4,7,5,2] => [3,2,1,1]
[1,3,6,5,2,4,7] => [3,1,3]
[1,3,6,5,2,7,4] => [3,1,2,1]
[1,3,6,5,4,2,7] => [3,1,1,2]
[1,3,6,5,4,7,2] => [3,1,2,1]
[1,3,6,5,7,2,4] => [3,2,2]
[1,3,6,5,7,4,2] => [3,2,1,1]
[1,3,6,7,2,4,5] => [4,3]
[1,3,6,7,2,5,4] => [4,2,1]
[1,3,6,7,4,2,5] => [4,1,2]
[1,3,6,7,4,5,2] => [4,2,1]
[1,3,6,7,5,2,4] => [4,1,2]
[1,3,6,7,5,4,2] => [4,1,1,1]
[1,3,7,2,4,5,6] => [3,4]
[1,3,7,2,4,6,5] => [3,3,1]
[1,3,7,2,5,4,6] => [3,2,2]
[1,3,7,2,5,6,4] => [3,3,1]
[1,3,7,2,6,4,5] => [3,2,2]
[1,3,7,2,6,5,4] => [3,2,1,1]
[1,3,7,4,2,5,6] => [3,1,3]
[1,3,7,4,2,6,5] => [3,1,2,1]
[1,3,7,4,5,2,6] => [3,2,2]
[1,3,7,4,5,6,2] => [3,3,1]
[1,3,7,4,6,2,5] => [3,2,2]
[1,3,7,4,6,5,2] => [3,2,1,1]
[1,3,7,5,2,4,6] => [3,1,3]
[1,3,7,5,2,6,4] => [3,1,2,1]
[1,3,7,5,4,2,6] => [3,1,1,2]
[1,3,7,5,4,6,2] => [3,1,2,1]
[1,3,7,5,6,2,4] => [3,2,2]
[1,3,7,5,6,4,2] => [3,2,1,1]
[1,3,7,6,2,4,5] => [3,1,3]
[1,3,7,6,2,5,4] => [3,1,2,1]
[1,3,7,6,4,2,5] => [3,1,1,2]
[1,3,7,6,4,5,2] => [3,1,2,1]
[1,3,7,6,5,2,4] => [3,1,1,2]
[1,3,7,6,5,4,2] => [3,1,1,1,1]
[1,4,2,3,5,6,7] => [2,5]
[1,4,2,3,5,7,6] => [2,4,1]
[1,4,2,3,6,5,7] => [2,3,2]
[1,4,2,3,6,7,5] => [2,4,1]
[1,4,2,3,7,5,6] => [2,3,2]
[1,4,2,3,7,6,5] => [2,3,1,1]
[1,4,2,5,3,6,7] => [2,2,3]
[1,4,2,5,3,7,6] => [2,2,2,1]
[1,4,2,5,6,3,7] => [2,3,2]
[1,4,2,5,6,7,3] => [2,4,1]
[1,4,2,5,7,3,6] => [2,3,2]
[1,4,2,5,7,6,3] => [2,3,1,1]
[1,4,2,6,3,5,7] => [2,2,3]
[1,4,2,6,3,7,5] => [2,2,2,1]
[1,4,2,6,5,3,7] => [2,2,1,2]
[1,4,2,6,5,7,3] => [2,2,2,1]
[1,4,2,6,7,3,5] => [2,3,2]
[1,4,2,6,7,5,3] => [2,3,1,1]
[1,4,2,7,3,5,6] => [2,2,3]
[1,4,2,7,3,6,5] => [2,2,2,1]
[1,4,2,7,5,3,6] => [2,2,1,2]
[1,4,2,7,5,6,3] => [2,2,2,1]
[1,4,2,7,6,3,5] => [2,2,1,2]
[1,4,2,7,6,5,3] => [2,2,1,1,1]
[1,4,3,2,5,6,7] => [2,1,4]
[1,4,3,2,5,7,6] => [2,1,3,1]
[1,4,3,2,6,5,7] => [2,1,2,2]
[1,4,3,2,6,7,5] => [2,1,3,1]
[1,4,3,2,7,5,6] => [2,1,2,2]
[1,4,3,2,7,6,5] => [2,1,2,1,1]
[1,4,3,5,2,6,7] => [2,2,3]
[1,4,3,5,2,7,6] => [2,2,2,1]
[1,4,3,5,6,2,7] => [2,3,2]
[1,4,3,5,6,7,2] => [2,4,1]
[1,4,3,5,7,2,6] => [2,3,2]
[1,4,3,5,7,6,2] => [2,3,1,1]
[1,4,3,6,2,5,7] => [2,2,3]
[1,4,3,6,2,7,5] => [2,2,2,1]
[1,4,3,6,5,2,7] => [2,2,1,2]
[1,4,3,6,5,7,2] => [2,2,2,1]
[1,4,3,6,7,2,5] => [2,3,2]
[1,4,3,6,7,5,2] => [2,3,1,1]
[1,4,3,7,2,5,6] => [2,2,3]
[1,4,3,7,2,6,5] => [2,2,2,1]
[1,4,3,7,5,2,6] => [2,2,1,2]
[1,4,3,7,5,6,2] => [2,2,2,1]
[1,4,3,7,6,2,5] => [2,2,1,2]
[1,4,3,7,6,5,2] => [2,2,1,1,1]
[1,4,5,2,3,6,7] => [3,4]
[1,4,5,2,3,7,6] => [3,3,1]
[1,4,5,2,6,3,7] => [3,2,2]
[1,4,5,2,6,7,3] => [3,3,1]
[1,4,5,2,7,3,6] => [3,2,2]
[1,4,5,2,7,6,3] => [3,2,1,1]
[1,4,5,3,2,6,7] => [3,1,3]
[1,4,5,3,2,7,6] => [3,1,2,1]
[1,4,5,3,6,2,7] => [3,2,2]
[1,4,5,3,6,7,2] => [3,3,1]
[1,4,5,3,7,2,6] => [3,2,2]
[1,4,5,3,7,6,2] => [3,2,1,1]
[1,4,5,6,2,3,7] => [4,3]
[1,4,5,6,2,7,3] => [4,2,1]
[1,4,5,6,3,2,7] => [4,1,2]
[1,4,5,6,3,7,2] => [4,2,1]
[1,4,5,6,7,2,3] => [5,2]
[1,4,5,6,7,3,2] => [5,1,1]
[1,4,5,7,2,3,6] => [4,3]
[1,4,5,7,2,6,3] => [4,2,1]
[1,4,5,7,3,2,6] => [4,1,2]
[1,4,5,7,3,6,2] => [4,2,1]
[1,4,5,7,6,2,3] => [4,1,2]
[1,4,5,7,6,3,2] => [4,1,1,1]
[1,4,6,2,3,5,7] => [3,4]
[1,4,6,2,3,7,5] => [3,3,1]
[1,4,6,2,5,3,7] => [3,2,2]
[1,4,6,2,5,7,3] => [3,3,1]
[1,4,6,2,7,3,5] => [3,2,2]
[1,4,6,2,7,5,3] => [3,2,1,1]
[1,4,6,3,2,5,7] => [3,1,3]
[1,4,6,3,2,7,5] => [3,1,2,1]
[1,4,6,3,5,2,7] => [3,2,2]
[1,4,6,3,5,7,2] => [3,3,1]
[1,4,6,3,7,2,5] => [3,2,2]
[1,4,6,3,7,5,2] => [3,2,1,1]
[1,4,6,5,2,3,7] => [3,1,3]
[1,4,6,5,2,7,3] => [3,1,2,1]
[1,4,6,5,3,2,7] => [3,1,1,2]
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Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Properties
surjectiveA map $\phi: A \rightarrow B$ is surjective if for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
Code
def descents_composition(elt):
    return elt.descents_composition()
Updated
May 16, 2019 at 07:57 by Christian Stump