- FindStat

Identifier

Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths

Images

[1] => [1,0] => [2,1] => [1,1,0,0]

[1,1] => [1,0,1,0] => [3,1,2] => [1,1,1,0,0,0]

[2] => [1,1,0,0] => [2,3,1] => [1,1,0,1,0,0]

[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [1,1,1,1,0,0,0,0]

[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [1,1,1,0,0,1,0,0]

[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [1,1,0,1,1,0,0,0]

[3] => [1,1,1,0,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0]

[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]

[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]

[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0]

[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0]

[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0]

[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0]

[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]

[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]

[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0]

[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0]

[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0]

[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0]

[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]

[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]

[1,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0]

[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0]

[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0]

[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]

[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0]

[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0]

[3,2] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0]

[4,1] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0]

[5] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]

[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]

[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]

[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]

[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]

[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]

[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]

[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]

[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]

[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]

[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0]

[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0]

[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]

[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0]

[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]

[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]

[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]

[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]

[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]

[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0]

[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]

[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]

[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0]

[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]

[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]

[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]

[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]

[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]

[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]

[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]

[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]

[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]

[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]

[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]

[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]

[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]

[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]

[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]

[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]

[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]

[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]

[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]

[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]

[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]

[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]

[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]

[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]

[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]

[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]

[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]

[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]

[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]

[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]

[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]

[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]

[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]

[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]

[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]

[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]

[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]

[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]

[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]

[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]

[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]

[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]

[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]

[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]

[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]

>>> Load all 234 entries. <<<

[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]

[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]

[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]

[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]

[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]

[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]

[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]

[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]

[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]

[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]

[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]

[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]

[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]

[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]

[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]

[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]

[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]

[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]

[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]

[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]

[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]

[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]

[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]

[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]

[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]

[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]

[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]

[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]

[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]

[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]

[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]

[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]

[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,1,2,3,8,4,6,9,7] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]

[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]

[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]

[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]

[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,9,3,8] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]

[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]

[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]

[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,8] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]

[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => [1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]

[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,5,6,9,2,7,8] => [1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]

[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]

[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]

[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,7,1,3,4,5,9,6,8] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]

[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,7,1,3,4,5,8,9,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]

[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,6,1,3,4,9,5,7,8] => [1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]

[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]

[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]

[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8] => [1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]

[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]

[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]

[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,8,1,4,5,6,9,7] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]

[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]

[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]

[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]

[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]

[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]

[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]

[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]

[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]

[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] => [9,1,2,3,4,5,6,7,10,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]

[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]

[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] => [7,1,2,3,4,5,9,6,10,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]

[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]

[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]

[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => [1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]

[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]

[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[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] => [3,1,9,2,4,5,6,7,10,8] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]

[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => [1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]

[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]

[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] => [3,1,4,10,2,5,6,7,8,9] => [1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[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] => [2,10,1,3,4,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]

[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] => [2,9,1,3,4,5,6,7,10,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]

[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] => [2,8,1,3,4,5,6,10,7,9] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]

[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]

[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]

[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[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] => [2,3,10,1,4,5,6,7,8,9] => [1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]

[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]

[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => [1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]

[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => [1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]

[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]

[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]

[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]

[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]

[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]

[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] => [10,1,2,3,4,5,6,7,8,11,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]

[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]

[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,11,2,10] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[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] => [2,11,1,3,4,5,6,7,8,9,10] => [1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]

[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] => [2,10,1,3,4,5,6,7,8,11,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]

[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[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] => [2,3,11,1,4,5,6,7,8,9,10] => [1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]

[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,11,1,5,6,7,8,9,10] => [1,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]

[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,11,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]

[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,11,1,6,7,8,9,10] => [1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]

[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]

[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,11,1,7,8,9,10] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]

[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]

[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,11,1,8,9,10] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]

[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,7,9,1,10,11,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]

[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,8,11,1,9,10] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]

[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]

[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]

[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]

[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] => [11,1,2,3,4,5,6,7,8,9,12,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]

[1,2,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]

Map

bounce path

Description

The bounce path determined by an integer composition.

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.