Identifier
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Images
[1,0] => [1,1,0,0] => [1,2] => [1]
[1,0,1,0] => [1,1,0,1,0,0] => [2,1,3] => [2,1]
[1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => [1,2]
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1]
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1]
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,2]
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3]
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3]
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1]
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,4,2,1]
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [4,2,3,1]
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,2,4,1]
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [2,3,4,1]
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [4,3,1,2]
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,4,1,2]
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [4,2,1,3]
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4]
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,3,1,4]
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [4,1,2,3]
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,2,4]
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4]
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4]
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,5,3,2,1]
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [5,3,4,2,1]
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,3,5,2,1]
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [3,4,5,2,1]
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [5,4,2,3,1]
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [4,5,2,3,1]
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [5,3,2,4,1]
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [4,3,2,5,1]
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,4,2,5,1]
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [5,2,3,4,1]
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [4,2,3,5,1]
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [3,2,4,5,1]
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [2,3,4,5,1]
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [5,4,3,1,2]
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [4,5,3,1,2]
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,3,4,1,2]
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [4,3,5,1,2]
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [3,4,5,1,2]
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [5,4,2,1,3]
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [4,5,2,1,3]
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [5,3,2,1,4]
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5]
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,4,2,1,5]
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [5,2,3,1,4]
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [4,2,3,1,5]
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,2,4,1,5]
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,3,4,1,5]
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [5,4,1,2,3]
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,3]
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [5,3,1,2,4]
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,3,1,2,5]
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [3,4,1,2,5]
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [5,2,1,3,4]
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [4,2,1,3,5]
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5]
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [2,3,1,4,5]
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4]
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5]
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5]
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5]
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [6,3,4,5,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [5,3,4,6,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [6,5,4,2,3,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [6,4,5,2,3,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [5,4,6,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [4,5,6,2,3,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [6,5,3,2,4,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [5,6,3,2,4,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [6,3,4,2,5,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [6,5,2,3,4,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [5,6,2,3,4,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [6,4,2,3,5,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [6,3,2,4,5,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1]
>>> Load all 335 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [6,2,3,4,5,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [6,4,5,3,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [5,4,6,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [4,5,6,3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [6,5,3,4,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [6,4,3,5,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [5,4,3,6,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [6,3,4,5,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3]
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [5,6,4,2,1,3]
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [6,4,5,2,1,3]
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [5,4,6,2,1,3]
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3]
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [6,5,3,2,1,4]
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [5,6,3,2,1,4]
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6]
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [6,3,4,2,1,5]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6]
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [6,5,2,3,1,4]
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [5,6,2,3,1,4]
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6]
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6]
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [5,6,4,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [6,4,5,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [5,4,6,1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [6,5,3,1,2,4]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [5,6,3,1,2,4]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [6,3,4,1,2,5]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6]
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [6,5,2,1,3,4]
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [5,6,2,1,3,4]
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6]
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6]
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [6,5,1,2,3,4]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [5,6,1,2,3,4]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6]
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [7,4,5,6,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [7,5,6,3,4,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [5,6,7,3,4,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [7,6,4,3,5,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [7,5,4,3,6,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [7,6,3,4,5,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [6,7,5,4,2,3,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [5,6,7,4,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [7,6,4,5,2,3,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [6,7,4,5,2,3,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [5,6,4,7,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [7,4,5,6,2,3,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [6,5,7,3,2,4,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [5,6,7,3,2,4,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [6,7,3,4,2,5,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [5,6,3,4,2,7,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [7,6,5,2,3,4,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [6,7,5,2,3,4,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [7,5,6,2,3,4,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [6,5,7,2,3,4,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [5,6,7,2,3,4,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [7,4,5,2,3,6,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [7,5,6,4,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [7,4,5,6,3,1,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [7,6,5,4,2,1,3]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [6,5,7,4,2,1,3]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [7,5,4,6,2,1,3]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [7,4,5,6,2,1,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [7,6,4,3,2,1,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [4,2,3,5,6,1,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [5,6,7,4,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [5,6,4,7,1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [7,4,5,6,1,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [5,4,6,7,1,2,3]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [5,6,7,3,1,2,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [7,6,4,3,1,2,5]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [5,6,4,3,1,2,7]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [5,4,6,3,1,2,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [5,6,3,4,1,2,7]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [5,4,3,6,1,2,7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [5,6,7,2,1,3,4]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [5,6,4,2,1,3,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [5,4,6,2,1,3,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [5,6,3,2,1,4,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [7,4,3,2,1,5,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [6,4,3,2,1,5,7]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [4,5,2,3,1,6,7]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [5,2,3,4,1,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [6,7,5,1,2,3,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [7,5,6,1,2,3,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [6,5,7,1,2,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [5,6,7,1,2,3,4]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [4,5,6,1,2,3,7]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [7,5,3,1,2,4,6]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [6,4,3,1,2,5,7]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [6,2,3,1,4,5,7]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [6,7,1,2,3,4,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [7,5,1,2,3,4,6]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [6,4,1,2,3,5,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [7,3,1,2,4,5,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [5,3,1,2,4,6,7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [3,4,1,2,5,6,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [8,7,6,4,5,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [8,7,5,4,6,3,2,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [8,7,6,5,4,3,1,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [7,8,5,6,3,4,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [5,6,7,8,1,2,3,4]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [5,6,3,4,1,2,7,8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [4,5,6,1,2,3,7,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [7,8,1,2,3,4,5,6]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [8,9,1,2,3,4,5,6,7]
[] => [1,0] => [1] => []
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [7,8,5,6,3,4,1,2,9]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [5,6,7,8,1,2,3,4,9]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [4,5,6,1,2,3,7,8,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [3,4,1,2,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [9,8,7,5,6,4,3,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [7,8,9,4,5,6,1,2,3]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.