Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Images
[1] => [1,0] => [2,1] => [2,1]
[1,1] => [1,0,1,0] => [3,1,2] => [2,3,1]
[2] => [1,1,0,0] => [2,3,1] => [3,1,2]
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [2,3,4,1]
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [2,4,1,3]
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2]
[3] => [1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1]
[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4]
[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [2,4,1,5,3]
[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [2,5,1,3,4]
[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,1,4,5,2]
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4]
[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [4,1,2,5,3]
[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4]
[5] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5]
[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] => [2,3,4,5,6,7,1]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6]
[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] => [2,3,4,5,6,7,8,1]
[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] => [2,3,4,5,6,8,1,7]
[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] => [2,3,4,5,7,1,8,6]
[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] => [2,3,4,5,8,1,6,7]
[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] => [2,3,4,6,1,7,8,5]
[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] => [2,3,4,6,1,8,5,7]
[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] => [2,3,4,7,1,5,8,6]
[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] => [2,3,4,8,1,5,6,7]
[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] => [2,3,5,1,6,7,8,4]
[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] => [2,3,5,1,6,8,4,7]
[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] => [2,3,5,1,7,4,8,6]
[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] => [2,3,5,1,8,4,6,7]
[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] => [2,3,6,1,4,7,8,5]
[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] => [2,3,6,1,4,8,5,7]
[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] => [2,3,7,1,4,5,8,6]
[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] => [2,3,8,1,4,5,6,7]
[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] => [2,4,1,5,6,7,8,3]
[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] => [2,4,1,5,6,8,3,7]
[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] => [2,4,1,5,7,3,8,6]
[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] => [2,4,1,5,8,3,6,7]
[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] => [2,4,1,6,3,7,8,5]
[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] => [2,4,1,6,3,8,5,7]
[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] => [2,4,1,7,3,5,8,6]
[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] => [2,4,1,8,3,5,6,7]
[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] => [2,5,1,3,6,7,8,4]
[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] => [2,5,1,3,6,8,4,7]
[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] => [2,5,1,3,7,4,8,6]
[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] => [2,5,1,3,8,4,6,7]
[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] => [2,6,1,3,4,7,8,5]
[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] => [2,6,1,3,4,8,5,7]
[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] => [2,7,1,3,4,5,8,6]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7]
[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] => [3,1,4,5,6,7,8,2]
[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] => [3,1,4,5,6,8,2,7]
[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] => [3,1,4,5,7,2,8,6]
[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] => [3,1,4,5,8,2,6,7]
[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] => [3,1,4,6,2,7,8,5]
[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] => [3,1,4,6,2,8,5,7]
>>> Load all 330 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] => [3,1,4,7,2,5,8,6]
[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] => [3,1,4,8,2,5,6,7]
[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] => [3,1,5,2,6,7,8,4]
[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] => [3,1,5,2,6,8,4,7]
[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] => [3,1,5,2,7,4,8,6]
[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] => [3,1,5,2,8,4,6,7]
[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] => [3,1,6,2,4,7,8,5]
[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] => [3,1,6,2,4,8,5,7]
[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] => [3,1,7,2,4,5,8,6]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [3,1,8,2,4,5,6,7]
[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] => [4,1,2,5,6,7,8,3]
[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] => [4,1,2,5,6,8,3,7]
[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] => [4,1,2,5,7,3,8,6]
[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] => [4,1,2,5,8,3,6,7]
[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] => [4,1,2,6,3,7,8,5]
[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] => [4,1,2,6,3,8,5,7]
[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] => [4,1,2,7,3,5,8,6]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [4,1,2,8,3,5,6,7]
[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] => [5,1,2,3,6,7,8,4]
[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] => [5,1,2,3,6,8,4,7]
[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] => [5,1,2,3,7,4,8,6]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [5,1,2,3,8,4,6,7]
[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] => [6,1,2,3,4,7,8,5]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [6,1,2,3,4,8,5,7]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [7,1,2,3,4,5,8,6]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7]
[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] => [2,3,4,5,6,7,8,9,1]
[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] => [2,3,4,5,6,7,9,1,8]
[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] => [2,3,4,5,6,8,1,9,7]
[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] => [2,3,4,5,6,9,1,7,8]
[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] => [2,3,4,5,7,1,8,9,6]
[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] => [2,3,4,5,7,1,9,6,8]
[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] => [2,3,4,5,8,1,6,9,7]
[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] => [2,3,4,5,9,1,6,7,8]
[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] => [2,3,4,6,1,7,8,9,5]
[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] => [2,3,4,6,1,7,9,5,8]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [5,1,2,3,6,9,4,7,8] => [2,3,4,7,1,5,8,9,6]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,1,2,3,6,8,4,9,7] => [2,3,4,7,1,5,9,6,8]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,9,4,8] => [2,3,4,8,1,5,6,9,7]
[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] => [2,3,4,9,1,5,6,7,8]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [4,1,2,9,3,5,6,7,8] => [2,3,5,1,6,7,8,9,4]
[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] => [2,3,5,1,6,7,9,4,8]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [4,1,2,6,3,9,5,7,8] => [2,3,5,1,7,4,8,9,6]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,8,5,9,7] => [2,3,5,1,7,4,9,6,8]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,1,2,6,3,7,8,9,5] => [2,3,5,1,9,4,6,7,8]
[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] => [2,3,6,1,4,7,8,9,5]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,7,3,8,9,6] => [2,3,6,1,4,9,5,7,8]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,5,6,9,3,7,8] => [2,3,7,1,4,5,8,9,6]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,5,6,8,3,9,7] => [2,3,7,1,4,5,9,6,8]
[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] => [2,3,8,1,4,5,6,9,7]
[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] => [2,3,9,1,4,5,6,7,8]
[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] => [2,4,1,5,6,7,8,9,3]
[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] => [2,4,1,5,6,7,9,3,8]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,7,2,4,5,9,6,8] => [2,4,1,5,6,8,3,9,7]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,6,2,4,7,8,9,5] => [2,4,1,5,9,3,6,7,8]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,5,2,9,4,6,7,8] => [2,4,1,6,3,7,8,9,5]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,1,5,2,8,4,6,9,7] => [2,4,1,6,3,7,9,5,8]
[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] => [2,4,1,6,3,8,5,9,7]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,7,4,8,9,6] => [2,4,1,6,3,9,5,7,8]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,5,2,6,9,4,7,8] => [2,4,1,7,3,5,8,9,6]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,5,2,6,7,9,4,8] => [2,4,1,8,3,5,6,9,7]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5,2,6,7,8,9,4] => [2,4,1,9,3,5,6,7,8]
[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] => [2,5,1,3,6,7,8,9,4]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,4,7,2,5,8,9,6] => [2,5,1,3,6,9,4,7,8]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,4,6,2,8,5,9,7] => [2,5,1,3,7,4,9,6,8]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,7,9,5,8] => [2,5,1,3,8,4,6,9,7]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4,6,2,7,8,9,5] => [2,5,1,3,9,4,6,7,8]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,4,5,9,2,6,7,8] => [2,6,1,3,4,7,8,9,5]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,1,4,5,7,2,8,9,6] => [2,6,1,3,4,9,5,7,8]
[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] => [2,7,1,3,4,5,8,9,6]
[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] => [2,7,1,3,4,5,9,6,8]
[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] => [2,8,1,3,4,5,6,9,7]
[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] => [2,9,1,3,4,5,6,7,8]
[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] => [3,1,4,5,6,7,8,9,2]
[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] => [3,1,4,5,6,7,9,2,8]
[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] => [3,1,4,5,6,8,2,9,7]
[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] => [3,1,4,5,6,9,2,7,8]
[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] => [3,1,4,5,7,2,8,9,6]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,6,1,3,4,7,8,9,5] => [3,1,4,5,9,2,6,7,8]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,5,1,3,9,4,6,7,8] => [3,1,4,6,2,7,8,9,5]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,5,1,3,7,4,9,6,8] => [3,1,4,6,2,8,5,9,7]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,5,1,3,6,9,4,7,8] => [3,1,4,7,2,5,8,9,6]
[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] => [3,1,4,9,2,5,6,7,8]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,9,3,5,6,7,8] => [3,1,5,2,6,7,8,9,4]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,6,3,9,5,7,8] => [3,1,5,2,7,4,8,9,6]
[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] => [3,1,5,2,7,4,9,6,8]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,6,3,7,9,5,8] => [3,1,5,2,8,4,6,9,7]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,6,3,7,8,9,5] => [3,1,5,2,9,4,6,7,8]
[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] => [3,1,6,2,4,7,8,9,5]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,5,6,9,3,7,8] => [3,1,7,2,4,5,8,9,6]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,1,5,6,8,3,9,7] => [3,1,7,2,4,5,9,6,8]
[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] => [3,1,8,2,4,5,6,9,7]
[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] => [3,1,9,2,4,5,6,7,8]
[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] => [4,1,2,5,6,7,8,9,3]
[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] => [4,1,2,5,6,7,9,3,8]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,7,1,4,5,8,9,6] => [4,1,2,5,6,9,3,7,8]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,6,1,4,7,8,9,5] => [4,1,2,5,9,3,6,7,8]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,5,1,9,4,6,7,8] => [4,1,2,6,3,7,8,9,5]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,9,6,8] => [4,1,2,6,3,8,5,9,7]
[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] => [4,1,2,8,3,5,6,9,7]
[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] => [4,1,2,9,3,5,6,7,8]
[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] => [5,1,2,3,6,7,8,9,4]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [2,3,4,8,1,5,6,9,7] => [5,1,2,3,6,7,9,4,8]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [2,3,4,7,1,5,9,6,8] => [5,1,2,3,6,8,4,9,7]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [2,3,4,7,1,5,8,9,6] => [5,1,2,3,6,9,4,7,8]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [2,3,4,6,1,9,5,7,8] => [5,1,2,3,7,4,8,9,6]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,3,4,6,1,8,5,9,7] => [5,1,2,3,7,4,9,6,8]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,3,4,6,1,7,9,5,8] => [5,1,2,3,8,4,6,9,7]
[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] => [5,1,2,3,9,4,6,7,8]
[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] => [6,1,2,3,4,7,8,9,5]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,8,1,6,9,7] => [6,1,2,3,4,7,9,5,8]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [2,3,4,5,7,1,9,6,8] => [6,1,2,3,4,8,5,9,7]
[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] => [6,1,2,3,4,9,5,7,8]
[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] => [7,1,2,3,4,5,8,9,6]
[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] => [7,1,2,3,4,5,9,6,8]
[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] => [8,1,2,3,4,5,6,9,7]
[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] => [9,1,2,3,4,5,6,7,8]
[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] => [2,3,4,5,6,7,8,9,10,1]
[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] => [9,1,2,3,4,5,6,7,10,8] => [2,3,4,5,6,7,8,10,1,9]
[1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,1,2,3,4,5,6,10,7,9] => [2,3,4,5,6,7,9,1,10,8]
[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] => [2,3,4,5,6,7,10,1,8,9]
[1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,1,2,3,4,5,10,6,8,9] => [2,3,4,5,6,8,1,9,10,7]
[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] => [2,3,4,5,6,8,1,10,7,9]
[1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,1,2,3,4,5,8,10,6,9] => [2,3,4,5,6,9,1,7,10,8]
[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] => [2,3,4,5,6,10,1,7,8,9]
[1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,1,2,3,4,10,5,7,8,9] => [2,3,4,5,7,1,8,9,10,6]
[1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,10,7,9] => [2,3,4,5,7,1,9,6,10,8]
[1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,1,2,3,4,7,10,5,8,9] => [2,3,4,5,8,1,6,9,10,7]
[1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,1,2,3,4,7,9,5,10,8] => [2,3,4,5,8,1,6,10,7,9]
[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] => [2,3,4,5,10,1,6,7,8,9]
[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] => [2,3,4,6,1,7,8,9,10,5]
[1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,9,6,10,8] => [2,3,4,6,1,8,5,10,7,9]
[1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,10,4,7,8,9] => [2,3,4,7,1,5,8,9,10,6]
[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] => [2,3,4,10,1,5,6,7,8,9]
[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] => [2,3,5,1,6,7,8,9,10,4]
[1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,10,7,9] => [2,3,5,1,7,4,9,6,10,8]
[1,1,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,10,3,6,7,8,9] => [2,3,6,1,4,7,8,9,10,5]
[1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,7,3,9,6,10,8] => [2,3,6,1,4,8,5,10,7,9]
[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] => [2,3,10,1,4,5,6,7,8,9]
[1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,10,2,4,5,6,7,8,9] => [2,4,1,5,6,7,8,9,10,3]
[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] => [2,4,1,5,6,7,8,10,3,9]
[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] => [2,4,1,6,3,7,8,9,10,5]
[1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,4,10,6,8,9] => [2,4,1,6,3,8,5,9,10,7]
[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] => [2,4,1,6,3,8,5,10,7,9]
[1,2,2,3,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,7,4,8,10,6,9] => [2,4,1,6,3,9,5,7,10,8]
[1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,6,10,4,7,8,9] => [2,4,1,7,3,5,8,9,10,6]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5,2,6,7,8,9,10,4] => [2,4,1,10,3,5,6,7,8,9]
[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] => [2,5,1,3,6,7,8,9,10,4]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4,5,7,2,8,9,10,6] => [2,6,1,3,4,10,5,7,8,9]
[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] => [2,8,1,3,4,5,6,10,7,9]
[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] => [2,9,1,3,4,5,6,7,10,8]
[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] => [2,10,1,3,4,5,6,7,8,9]
[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] => [3,1,4,5,6,7,8,9,10,2]
[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] => [3,1,4,5,6,7,8,10,2,9]
[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] => [3,1,4,5,6,7,9,2,10,8]
[2,1,2,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,5,1,3,10,4,6,7,8,9] => [3,1,4,6,2,7,8,9,10,5]
[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] => [3,1,4,10,2,5,6,7,8,9]
[2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,10,3,5,6,7,8,9] => [3,1,5,2,6,7,8,9,10,4]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,6,3,10,5,7,8,9] => [3,1,5,2,7,4,8,9,10,6]
[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] => [3,1,5,2,7,4,9,6,10,8]
[2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,8,5,9,10,7] => [3,1,5,2,7,4,10,6,8,9]
[2,2,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,6,3,7,10,5,8,9] => [3,1,5,2,8,4,6,9,10,7]
[2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,10,3,6,7,8,9] => [3,1,6,2,4,7,8,9,10,5]
[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] => [3,1,9,2,4,5,6,7,10,8]
[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] => [3,1,10,2,4,5,6,7,8,9]
[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] => [4,1,2,5,6,7,8,9,10,3]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,9,6,10,8] => [4,1,2,6,3,8,5,10,7,9]
[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] => [4,1,2,10,3,5,6,7,8,9]
[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] => [5,1,2,3,6,7,8,9,10,4]
[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] => [5,1,2,3,10,4,6,7,8,9]
[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] => [6,1,2,3,4,7,8,9,10,5]
[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] => [6,1,2,3,4,10,5,7,8,9]
[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] => [7,1,2,3,4,5,8,9,10,6]
[6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,6,9,1,7,10,8] => [7,1,2,3,4,5,8,10,6,9]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [2,3,4,5,6,8,1,10,7,9] => [7,1,2,3,4,5,9,6,10,8]
[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] => [7,1,2,3,4,5,10,6,8,9]
[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] => [8,1,2,3,4,5,6,9,10,7]
[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] => [8,1,2,3,4,5,6,10,7,9]
[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] => [9,1,2,3,4,5,6,7,10,8]
[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] => [10,1,2,3,4,5,6,7,8,9]
[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] => [2,3,4,5,6,7,8,9,10,11,1]
[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] => [10,1,2,3,4,5,6,7,8,11,9] => [2,3,4,5,6,7,8,9,11,1,10]
[1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,1,2,3,4,5,6,7,11,8,10] => [2,3,4,5,6,7,8,10,1,11,9]
[1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [9,1,2,3,4,5,6,7,10,11,8] => [2,3,4,5,6,7,8,11,1,9,10]
[1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,1,2,3,4,5,6,11,7,9,10] => [2,3,4,5,6,7,9,1,10,11,8]
[1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,1,2,3,4,5,6,10,7,11,9] => [2,3,4,5,6,7,9,1,11,8,10]
[1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [8,1,2,3,4,5,6,9,10,11,7] => [2,3,4,5,6,7,11,1,8,9,10]
[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] => [2,3,4,5,6,8,1,9,10,11,7]
[1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [7,1,2,3,4,5,8,9,10,11,6] => [2,3,4,5,6,11,1,7,8,9,10]
[1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,11,5,7,8,9,10] => [2,3,4,5,7,1,8,9,10,11,6]
[1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,10,7,11,9] => [2,3,4,5,7,1,9,6,11,8,10]
[1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,11,5] => [2,3,4,5,11,1,6,7,8,9,10]
[1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,2,3,11,4,6,7,8,9,10] => [2,3,4,6,1,7,8,9,10,11,5]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,11,4] => [2,3,4,11,1,5,6,7,8,9,10]
[1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,11,3,5,6,7,8,9,10] => [2,3,5,1,6,7,8,9,10,11,4]
[1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,8,5,10,7,11,9] => [2,3,5,1,7,4,9,6,11,8,10]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,11,3] => [2,3,11,1,4,5,6,7,8,9,10]
[1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,11,2,4,5,6,7,8,9,10] => [2,4,1,5,6,7,8,9,10,11,3]
[1,2,2,1,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,11,4,6,7,8,9,10] => [2,4,1,6,3,7,8,9,10,11,5]
[1,2,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,11,6,8,9,10] => [2,4,1,6,3,8,5,9,10,11,7]
[1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,11,8,10] => [2,4,1,6,3,8,5,10,7,11,9]
[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] => [2,10,1,3,4,5,6,7,8,11,9]
[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] => [2,11,1,3,4,5,6,7,8,9,10]
[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] => [3,1,4,5,6,7,8,9,10,11,2]
[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] => [3,1,4,5,6,7,8,9,11,2,10]
[2,2,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,11,3,5,6,7,8,9,10] => [3,1,5,2,6,7,8,9,10,11,4]
[2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,6,3,11,5,7,8,9,10] => [3,1,5,2,7,4,8,9,10,11,6]
[2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,6,3,8,5,11,7,9,10] => [3,1,5,2,7,4,9,6,10,11,8]
[2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,10,7,11,9] => [3,1,5,2,7,4,9,6,11,8,10]
[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] => [3,1,11,2,4,5,6,7,8,9,10]
[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] => [4,1,2,5,6,7,8,9,10,11,3]
[3,2,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,9,6,11,8,10] => [4,1,2,6,3,8,5,10,7,11,9]
[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] => [4,1,2,11,3,5,6,7,8,9,10]
[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] => [5,1,2,3,6,7,8,9,10,11,4]
[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] => [5,1,2,3,11,4,6,7,8,9,10]
[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] => [6,1,2,3,4,7,8,9,10,11,5]
[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] => [6,1,2,3,4,11,5,7,8,9,10]
[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] => [7,1,2,3,4,5,8,9,10,11,6]
[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] => [7,1,2,3,4,5,11,6,8,9,10]
[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] => [8,1,2,3,4,5,6,9,10,11,7]
[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] => [8,1,2,3,4,5,6,11,7,9,10]
[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] => [9,1,2,3,4,5,6,7,10,11,8]
[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] => [9,1,2,3,4,5,6,7,11,8,10]
[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] => [10,1,2,3,4,5,6,7,8,11,9]
[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] => [11,1,2,3,4,5,6,7,8,9,10]
[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] => [2,12,1,3,4,5,6,7,8,9,10,11]
[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] => [11,1,2,3,4,5,6,7,8,9,12,10]
[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] => [2,3,4,5,6,7,8,9,10,12,1,11]
[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] => [2,4,1,6,3,8,5,10,7,12,9,11]
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
inverse
Description
Sends a permutation to its inverse.