Identifier
Values
[1] => [1] => [1,0] => 1
[1,1] => [2] => [1,1,0,0] => 2
[2] => [1,1] => [1,0,1,0] => 1
[1,1,1] => [3] => [1,1,1,0,0,0] => 3
[1,2] => [2,1] => [1,1,0,0,1,0] => 1
[2,1] => [1,2] => [1,0,1,1,0,0] => 1
[3] => [1,1,1] => [1,0,1,0,1,0] => 1
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
[1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
>>> Load all 267 entries. <<<
[2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,2] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,2,1] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,2,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,2,2,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,2,1,1,2] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,5,1] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,6] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,2,1,1,1,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,2,1,1,3] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,1,2,1,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,2,1,2,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,2,1,3,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,1,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,2,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,2,2,3] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,2,3,1,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,3,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,2,4,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,2,5] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,3,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,3,1,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,3,1,2,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,3,1,3] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,2,1,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,3,2,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,3,4] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,4,1,1,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,4,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,4,2,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,4,3] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,5,1,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,5,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,7] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,1,1,2,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[2,1,1,1,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[2,1,1,2,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[2,1,1,2,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[2,1,1,3,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[2,1,1,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[2,1,2,1,1,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[2,1,2,2,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[2,1,2,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[2,1,3,1,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[2,1,3,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[2,1,4,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[2,1,5] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[2,2,1,1,1,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,2,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,2,1,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,2,1,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,2,2,1,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[2,2,3,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[2,2,4] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,3,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[2,3,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,3,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[2,3,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[2,4,1,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[2,5,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[2,6] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[3,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,1,2,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,1,2,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[3,1,2,2] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,1,3,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[3,1,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,2,1,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,2] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[3,2,2,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[3,3,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,3,2] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[3,4,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[3,5] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[4,1,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[4,1,1,2] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[4,1,2,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[4,1,3] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[4,2,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[4,2,2] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[4,3,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[5,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[5,1,2] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[5,2,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[5,3] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[6,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[6,2] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[7,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[8] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,2] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,2,1] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,7] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,1,1,1] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,2,1,1,1,1,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,6,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,7,1] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,8] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,1,1,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[2,1,1,1,1,1,2] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[2,1,1,1,1,2,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[2,1,1,1,1,3] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[2,1,6] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,2,1,1,1,1,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[2,6,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,1,1,1,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[3,1,1,1,1,2] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[6,2,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[8,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,2] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,2,1] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 2
[1,1,8] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,1,1,1,1] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,8,1] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,9] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,1,1,1,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[2,1,1,1,1,1,1,2] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[2,1,1,1,1,1,3] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[3,1,1,1,1,1,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[3,1,1,1,1,1,2] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[9,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[10,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,2] => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[2,1,1,1,1,1,1,1,1,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
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Description
The length of the minimal rise of a Dyck path.
For the length of a maximal rise, see St000444The length of the maximal rise of a Dyck path..
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
Map
bounce path
Description
The bounce path determined by an integer composition.