Identifier
Identifier
Mp00067: Permutations —Foata bijection⟶ Permutations
Images
[1] => [1]
[1,2] => [1,2]
[2,1] => [2,1]
[1,2,3] => [1,2,3]
[1,3,2] => [3,1,2]
[2,1,3] => [2,1,3]
[2,3,1] => [2,3,1]
[3,1,2] => [1,3,2]
[3,2,1] => [3,2,1]
[1,2,3,4] => [1,2,3,4]
[1,2,4,3] => [4,1,2,3]
[1,3,2,4] => [3,1,2,4]
[1,3,4,2] => [3,1,4,2]
[1,4,2,3] => [1,4,2,3]
[1,4,3,2] => [4,3,1,2]
[2,1,3,4] => [2,1,3,4]
[2,1,4,3] => [4,2,1,3]
[2,3,1,4] => [2,3,1,4]
[2,3,4,1] => [2,3,4,1]
[2,4,1,3] => [2,1,4,3]
[2,4,3,1] => [4,2,3,1]
[3,1,2,4] => [1,3,2,4]
[3,1,4,2] => [3,4,1,2]
[3,2,1,4] => [3,2,1,4]
[3,2,4,1] => [3,2,4,1]
[3,4,1,2] => [1,3,4,2]
[3,4,2,1] => [3,4,2,1]
[4,1,2,3] => [1,2,4,3]
[4,1,3,2] => [4,1,3,2]
[4,2,1,3] => [2,4,1,3]
[4,2,3,1] => [2,4,3,1]
[4,3,1,2] => [1,4,3,2]
[4,3,2,1] => [4,3,2,1]
[1,2,3,4,5] => [1,2,3,4,5]
[1,2,3,5,4] => [5,1,2,3,4]
[1,2,4,3,5] => [4,1,2,3,5]
[1,2,4,5,3] => [4,1,2,5,3]
[1,2,5,3,4] => [1,5,2,3,4]
[1,2,5,4,3] => [5,4,1,2,3]
[1,3,2,4,5] => [3,1,2,4,5]
[1,3,2,5,4] => [5,3,1,2,4]
[1,3,4,2,5] => [3,1,4,2,5]
[1,3,4,5,2] => [3,1,4,5,2]
[1,3,5,2,4] => [3,1,2,5,4]
[1,3,5,4,2] => [5,3,1,4,2]
[1,4,2,3,5] => [1,4,2,3,5]
[1,4,2,5,3] => [4,5,1,2,3]
[1,4,3,2,5] => [4,3,1,2,5]
[1,4,3,5,2] => [4,3,1,5,2]
[1,4,5,2,3] => [1,4,2,5,3]
[1,4,5,3,2] => [4,5,1,3,2]
[1,5,2,3,4] => [1,2,5,3,4]
[1,5,2,4,3] => [5,1,4,2,3]
[1,5,3,2,4] => [3,5,1,2,4]
[1,5,3,4,2] => [5,1,3,4,2]
[1,5,4,2,3] => [1,5,4,2,3]
[1,5,4,3,2] => [5,4,3,1,2]
[2,1,3,4,5] => [2,1,3,4,5]
[2,1,3,5,4] => [5,2,1,3,4]
[2,1,4,3,5] => [4,2,1,3,5]
[2,1,4,5,3] => [4,2,1,5,3]
[2,1,5,3,4] => [2,5,1,3,4]
[2,1,5,4,3] => [5,4,2,1,3]
[2,3,1,4,5] => [2,3,1,4,5]
[2,3,1,5,4] => [5,2,3,1,4]
[2,3,4,1,5] => [2,3,4,1,5]
[2,3,4,5,1] => [2,3,4,5,1]
[2,3,5,1,4] => [2,3,1,5,4]
[2,3,5,4,1] => [5,2,3,4,1]
[2,4,1,3,5] => [2,1,4,3,5]
[2,4,1,5,3] => [4,2,5,1,3]
[2,4,3,1,5] => [4,2,3,1,5]
[2,4,3,5,1] => [4,2,3,5,1]
[2,4,5,1,3] => [2,1,4,5,3]
[2,4,5,3,1] => [4,2,5,3,1]
[2,5,1,3,4] => [2,1,3,5,4]
[2,5,1,4,3] => [5,2,1,4,3]
[2,5,3,1,4] => [2,5,3,1,4]
[2,5,3,4,1] => [2,5,3,4,1]
[2,5,4,1,3] => [2,5,1,4,3]
[2,5,4,3,1] => [5,4,2,3,1]
[3,1,2,4,5] => [1,3,2,4,5]
[3,1,2,5,4] => [5,1,3,2,4]
[3,1,4,2,5] => [3,4,1,2,5]
[3,1,4,5,2] => [3,4,1,5,2]
[3,1,5,2,4] => [3,1,5,2,4]
[3,1,5,4,2] => [5,3,4,1,2]
[3,2,1,4,5] => [3,2,1,4,5]
[3,2,1,5,4] => [5,3,2,1,4]
[3,2,4,1,5] => [3,2,4,1,5]
[3,2,4,5,1] => [3,2,4,5,1]
[3,2,5,1,4] => [3,2,1,5,4]
[3,2,5,4,1] => [5,3,2,4,1]
[3,4,1,2,5] => [1,3,4,2,5]
[3,4,1,5,2] => [3,4,5,1,2]
[3,4,2,1,5] => [3,4,2,1,5]
[3,4,2,5,1] => [3,4,2,5,1]
[3,4,5,1,2] => [1,3,4,5,2]
[3,4,5,2,1] => [3,4,5,2,1]
[3,5,1,2,4] => [1,3,2,5,4]
[3,5,1,4,2] => [3,5,1,4,2]
[3,5,2,1,4] => [3,2,5,1,4]
[3,5,2,4,1] => [3,2,5,4,1]
[3,5,4,1,2] => [1,5,3,4,2]
[3,5,4,2,1] => [5,3,4,2,1]
[4,1,2,3,5] => [1,2,4,3,5]
[4,1,2,5,3] => [4,1,5,2,3]
[4,1,3,2,5] => [4,1,3,2,5]
[4,1,3,5,2] => [4,1,3,5,2]
[4,1,5,2,3] => [1,4,5,2,3]
[4,1,5,3,2] => [4,5,3,1,2]
[4,2,1,3,5] => [2,4,1,3,5]
[4,2,1,5,3] => [4,5,2,1,3]
[4,2,3,1,5] => [2,4,3,1,5]
[4,2,3,5,1] => [2,4,3,5,1]
[4,2,5,1,3] => [2,4,1,5,3]
[4,2,5,3,1] => [4,5,2,3,1]
[4,3,1,2,5] => [1,4,3,2,5]
[4,3,1,5,2] => [4,3,5,1,2]
[4,3,2,1,5] => [4,3,2,1,5]
[4,3,2,5,1] => [4,3,2,5,1]
[4,3,5,1,2] => [1,4,3,5,2]
[4,3,5,2,1] => [4,3,5,2,1]
[4,5,1,2,3] => [1,2,4,5,3]
[4,5,1,3,2] => [4,1,5,3,2]
[4,5,2,1,3] => [2,4,5,1,3]
[4,5,2,3,1] => [2,4,5,3,1]
[4,5,3,1,2] => [1,4,5,3,2]
[4,5,3,2,1] => [4,5,3,2,1]
[5,1,2,3,4] => [1,2,3,5,4]
[5,1,2,4,3] => [5,1,2,4,3]
[5,1,3,2,4] => [1,5,3,2,4]
[5,1,3,4,2] => [3,1,5,4,2]
[5,1,4,2,3] => [1,5,2,4,3]
[5,1,4,3,2] => [5,4,1,3,2]
[5,2,1,3,4] => [2,1,5,3,4]
[5,2,1,4,3] => [5,2,4,1,3]
[5,2,3,1,4] => [2,3,5,1,4]
[5,2,3,4,1] => [2,3,5,4,1]
[5,2,4,1,3] => [2,1,5,4,3]
[5,2,4,3,1] => [5,2,4,3,1]
[5,3,1,2,4] => [1,3,5,2,4]
[5,3,1,4,2] => [3,5,4,1,2]
[5,3,2,1,4] => [3,5,2,1,4]
[5,3,2,4,1] => [3,5,2,4,1]
[5,3,4,1,2] => [1,3,5,4,2]
[5,3,4,2,1] => [3,5,4,2,1]
[5,4,1,2,3] => [1,2,5,4,3]
[5,4,1,3,2] => [5,1,4,3,2]
[5,4,2,1,3] => [2,5,4,1,3]
[5,4,2,3,1] => [2,5,4,3,1]
[5,4,3,1,2] => [1,5,4,3,2]
[5,4,3,2,1] => [5,4,3,2,1]
[1,2,3,4,5,6] => [1,2,3,4,5,6]
[1,2,3,4,6,5] => [6,1,2,3,4,5]
[1,2,3,5,4,6] => [5,1,2,3,4,6]
[1,2,3,5,6,4] => [5,1,2,3,6,4]
[1,2,3,6,4,5] => [1,6,2,3,4,5]
[1,2,3,6,5,4] => [6,5,1,2,3,4]
[1,2,4,3,5,6] => [4,1,2,3,5,6]
[1,2,4,3,6,5] => [6,4,1,2,3,5]
[1,2,4,5,3,6] => [4,1,2,5,3,6]
[1,2,4,5,6,3] => [4,1,2,5,6,3]
[1,2,4,6,3,5] => [4,1,2,3,6,5]
[1,2,4,6,5,3] => [6,4,1,2,5,3]
[1,2,5,3,4,6] => [1,5,2,3,4,6]
[1,2,5,3,6,4] => [5,6,1,2,3,4]
[1,2,5,4,3,6] => [5,4,1,2,3,6]
[1,2,5,4,6,3] => [5,4,1,2,6,3]
[1,2,5,6,3,4] => [1,5,2,3,6,4]
[1,2,5,6,4,3] => [5,6,1,2,4,3]
[1,2,6,3,4,5] => [1,2,6,3,4,5]
[1,2,6,3,5,4] => [6,1,5,2,3,4]
[1,2,6,4,3,5] => [4,6,1,2,3,5]
[1,2,6,4,5,3] => [6,1,4,2,5,3]
[1,2,6,5,3,4] => [1,6,5,2,3,4]
[1,2,6,5,4,3] => [6,5,4,1,2,3]
[1,3,2,4,5,6] => [3,1,2,4,5,6]
[1,3,2,4,6,5] => [6,3,1,2,4,5]
[1,3,2,5,4,6] => [5,3,1,2,4,6]
[1,3,2,5,6,4] => [5,3,1,2,6,4]
[1,3,2,6,4,5] => [3,6,1,2,4,5]
[1,3,2,6,5,4] => [6,5,3,1,2,4]
[1,3,4,2,5,6] => [3,1,4,2,5,6]
[1,3,4,2,6,5] => [6,3,1,4,2,5]
[1,3,4,5,2,6] => [3,1,4,5,2,6]
[1,3,4,5,6,2] => [3,1,4,5,6,2]
[1,3,4,6,2,5] => [3,1,4,2,6,5]
[1,3,4,6,5,2] => [6,3,1,4,5,2]
[1,3,5,2,4,6] => [3,1,2,5,4,6]
[1,3,5,2,6,4] => [5,3,1,6,2,4]
[1,3,5,4,2,6] => [5,3,1,4,2,6]
[1,3,5,4,6,2] => [5,3,1,4,6,2]
[1,3,5,6,2,4] => [3,1,2,5,6,4]
[1,3,5,6,4,2] => [5,3,1,6,4,2]
[1,3,6,2,4,5] => [3,1,2,4,6,5]
[1,3,6,2,5,4] => [6,3,1,2,5,4]
[1,3,6,4,2,5] => [3,6,1,4,2,5]
[1,3,6,4,5,2] => [6,1,3,4,5,2]
[1,3,6,5,2,4] => [3,6,1,2,5,4]
[1,3,6,5,4,2] => [6,5,3,1,4,2]
[1,4,2,3,5,6] => [1,4,2,3,5,6]
[1,4,2,3,6,5] => [6,1,4,2,3,5]
[1,4,2,5,3,6] => [4,5,1,2,3,6]
[1,4,2,5,6,3] => [4,5,1,2,6,3]
[1,4,2,6,3,5] => [4,1,6,2,3,5]
[1,4,2,6,5,3] => [6,4,5,1,2,3]
[1,4,3,2,5,6] => [4,3,1,2,5,6]
[1,4,3,2,6,5] => [6,4,3,1,2,5]
[1,4,3,5,2,6] => [4,3,1,5,2,6]
[1,4,3,5,6,2] => [4,3,1,5,6,2]
[1,4,3,6,2,5] => [4,3,1,2,6,5]
[1,4,3,6,5,2] => [6,4,3,1,5,2]
[1,4,5,2,3,6] => [1,4,2,5,3,6]
[1,4,5,2,6,3] => [4,5,1,6,2,3]
[1,4,5,3,2,6] => [4,5,1,3,2,6]
[1,4,5,3,6,2] => [4,5,1,3,6,2]
[1,4,5,6,2,3] => [1,4,2,5,6,3]
[1,4,5,6,3,2] => [4,5,1,6,3,2]
[1,4,6,2,3,5] => [1,4,2,3,6,5]
[1,4,6,2,5,3] => [4,6,1,2,5,3]
[1,4,6,3,2,5] => [4,1,6,3,2,5]
[1,4,6,3,5,2] => [4,3,1,6,5,2]
[1,4,6,5,2,3] => [1,6,4,2,5,3]
[1,4,6,5,3,2] => [6,4,5,1,3,2]
[1,5,2,3,4,6] => [1,2,5,3,4,6]
[1,5,2,3,6,4] => [5,1,6,2,3,4]
[1,5,2,4,3,6] => [5,1,4,2,3,6]
[1,5,2,4,6,3] => [5,1,4,2,6,3]
[1,5,2,6,3,4] => [1,5,6,2,3,4]
[1,5,2,6,4,3] => [5,6,4,1,2,3]
[1,5,3,2,4,6] => [3,5,1,2,4,6]
[1,5,3,2,6,4] => [5,6,3,1,2,4]
[1,5,3,4,2,6] => [5,1,3,4,2,6]
[1,5,3,4,6,2] => [5,1,3,4,6,2]
[1,5,3,6,2,4] => [3,5,1,2,6,4]
[1,5,3,6,4,2] => [5,6,3,1,4,2]
[1,5,4,2,3,6] => [1,5,4,2,3,6]
[1,5,4,2,6,3] => [5,4,6,1,2,3]
[1,5,4,3,2,6] => [5,4,3,1,2,6]
[1,5,4,3,6,2] => [5,4,3,1,6,2]
[1,5,4,6,2,3] => [1,5,4,2,6,3]
[1,5,4,6,3,2] => [5,4,6,1,3,2]
[1,5,6,2,3,4] => [1,2,5,3,6,4]
[1,5,6,2,4,3] => [5,1,6,2,4,3]
[1,5,6,3,2,4] => [1,5,6,3,2,4]
[1,5,6,3,4,2] => [5,1,3,6,4,2]
[1,5,6,4,2,3] => [1,5,6,2,4,3]
[1,5,6,4,3,2] => [5,6,4,1,3,2]
[1,6,2,3,4,5] => [1,2,3,6,4,5]
[1,6,2,3,5,4] => [6,1,2,5,3,4]
[1,6,2,4,3,5] => [1,6,4,2,3,5]
[1,6,2,4,5,3] => [6,1,2,4,5,3]
[1,6,2,5,3,4] => [1,6,2,5,3,4]
[1,6,2,5,4,3] => [6,5,1,4,2,3]
[1,6,3,2,4,5] => [3,1,6,2,4,5]
[1,6,3,2,5,4] => [6,3,5,1,2,4]
[1,6,3,4,2,5] => [1,6,3,4,2,5]
[1,6,3,4,5,2] => [3,1,6,4,5,2]
[1,6,3,5,2,4] => [1,6,3,2,5,4]
[1,6,3,5,4,2] => [6,5,1,3,4,2]
[1,6,4,2,3,5] => [1,4,6,2,3,5]
[1,6,4,2,5,3] => [4,6,5,1,2,3]
[1,6,4,3,2,5] => [4,6,3,1,2,5]
[1,6,4,3,5,2] => [4,6,3,1,5,2]
[1,6,4,5,2,3] => [1,6,2,4,5,3]
[1,6,4,5,3,2] => [6,4,1,5,3,2]
[1,6,5,2,3,4] => [1,2,6,5,3,4]
[1,6,5,2,4,3] => [6,1,5,4,2,3]
[1,6,5,3,2,4] => [3,6,5,1,2,4]
[1,6,5,3,4,2] => [6,1,5,3,4,2]
[1,6,5,4,2,3] => [1,6,5,4,2,3]
[1,6,5,4,3,2] => [6,5,4,3,1,2]
[2,1,3,4,5,6] => [2,1,3,4,5,6]
[2,1,3,4,6,5] => [6,2,1,3,4,5]
[2,1,3,5,4,6] => [5,2,1,3,4,6]
[2,1,3,5,6,4] => [5,2,1,3,6,4]
[2,1,3,6,4,5] => [2,6,1,3,4,5]
[2,1,3,6,5,4] => [6,5,2,1,3,4]
[2,1,4,3,5,6] => [4,2,1,3,5,6]
[2,1,4,3,6,5] => [6,4,2,1,3,5]
[2,1,4,5,3,6] => [4,2,1,5,3,6]
[2,1,4,5,6,3] => [4,2,1,5,6,3]
[2,1,4,6,3,5] => [4,2,1,3,6,5]
[2,1,4,6,5,3] => [6,4,2,1,5,3]
[2,1,5,3,4,6] => [2,5,1,3,4,6]
[2,1,5,3,6,4] => [5,6,2,1,3,4]
[2,1,5,4,3,6] => [5,4,2,1,3,6]
[2,1,5,4,6,3] => [5,4,2,1,6,3]
[2,1,5,6,3,4] => [2,5,1,3,6,4]
[2,1,5,6,4,3] => [5,6,2,1,4,3]
[2,1,6,3,4,5] => [2,1,6,3,4,5]
[2,1,6,3,5,4] => [6,2,5,1,3,4]
[2,1,6,4,3,5] => [4,6,2,1,3,5]
[2,1,6,4,5,3] => [6,2,4,1,5,3]
[2,1,6,5,3,4] => [2,6,5,1,3,4]
[2,1,6,5,4,3] => [6,5,4,2,1,3]
[2,3,1,4,5,6] => [2,3,1,4,5,6]
[2,3,1,4,6,5] => [6,2,3,1,4,5]
[2,3,1,5,4,6] => [5,2,3,1,4,6]
[2,3,1,5,6,4] => [5,2,3,1,6,4]
[2,3,1,6,4,5] => [2,6,3,1,4,5]
[2,3,1,6,5,4] => [6,5,2,3,1,4]
[2,3,4,1,5,6] => [2,3,4,1,5,6]
[2,3,4,1,6,5] => [6,2,3,4,1,5]
[2,3,4,5,1,6] => [2,3,4,5,1,6]
[2,3,4,5,6,1] => [2,3,4,5,6,1]
[2,3,4,6,1,5] => [2,3,4,1,6,5]
[2,3,4,6,5,1] => [6,2,3,4,5,1]
[2,3,5,1,4,6] => [2,3,1,5,4,6]
[2,3,5,1,6,4] => [5,2,3,6,1,4]
[2,3,5,4,1,6] => [5,2,3,4,1,6]
[2,3,5,4,6,1] => [5,2,3,4,6,1]
[2,3,5,6,1,4] => [2,3,1,5,6,4]
[2,3,5,6,4,1] => [5,2,3,6,4,1]
[2,3,6,1,4,5] => [2,3,1,4,6,5]
[2,3,6,1,5,4] => [6,2,3,1,5,4]
[2,3,6,4,1,5] => [2,6,3,4,1,5]
[2,3,6,4,5,1] => [2,6,3,4,5,1]
[2,3,6,5,1,4] => [2,6,3,1,5,4]
[2,3,6,5,4,1] => [6,5,2,3,4,1]
[2,4,1,3,5,6] => [2,1,4,3,5,6]
[2,4,1,3,6,5] => [6,2,1,4,3,5]
[2,4,1,5,3,6] => [4,2,5,1,3,6]
[2,4,1,5,6,3] => [4,2,5,1,6,3]
[2,4,1,6,3,5] => [4,2,1,6,3,5]
[2,4,1,6,5,3] => [6,4,2,5,1,3]
[2,4,3,1,5,6] => [4,2,3,1,5,6]
[2,4,3,1,6,5] => [6,4,2,3,1,5]
[2,4,3,5,1,6] => [4,2,3,5,1,6]
[2,4,3,5,6,1] => [4,2,3,5,6,1]
[2,4,3,6,1,5] => [4,2,3,1,6,5]
[2,4,3,6,5,1] => [6,4,2,3,5,1]
[2,4,5,1,3,6] => [2,1,4,5,3,6]
[2,4,5,1,6,3] => [4,2,5,6,1,3]
[2,4,5,3,1,6] => [4,2,5,3,1,6]
[2,4,5,3,6,1] => [4,2,5,3,6,1]
[2,4,5,6,1,3] => [2,1,4,5,6,3]
[2,4,5,6,3,1] => [4,2,5,6,3,1]
[2,4,6,1,3,5] => [2,1,4,3,6,5]
[2,4,6,1,5,3] => [4,2,6,1,5,3]
[2,4,6,3,1,5] => [4,2,3,6,1,5]
[2,4,6,3,5,1] => [4,2,3,6,5,1]
[2,4,6,5,1,3] => [2,6,1,4,5,3]
[2,4,6,5,3,1] => [6,4,2,5,3,1]
[2,5,1,3,4,6] => [2,1,3,5,4,6]
[2,5,1,3,6,4] => [5,2,1,6,3,4]
[2,5,1,4,3,6] => [5,2,1,4,3,6]
[2,5,1,4,6,3] => [5,2,1,4,6,3]
[2,5,1,6,3,4] => [2,5,1,6,3,4]
[2,5,1,6,4,3] => [5,6,2,4,1,3]
[2,5,3,1,4,6] => [2,5,3,1,4,6]
[2,5,3,1,6,4] => [5,6,2,3,1,4]
[2,5,3,4,1,6] => [2,5,3,4,1,6]
[2,5,3,4,6,1] => [2,5,3,4,6,1]
[2,5,3,6,1,4] => [2,5,3,1,6,4]
[2,5,3,6,4,1] => [5,6,2,3,4,1]
[2,5,4,1,3,6] => [2,5,1,4,3,6]
[2,5,4,1,6,3] => [5,4,2,6,1,3]
[2,5,4,3,1,6] => [5,4,2,3,1,6]
[2,5,4,3,6,1] => [5,4,2,3,6,1]
[2,5,4,6,1,3] => [2,5,1,4,6,3]
[2,5,4,6,3,1] => [5,4,2,6,3,1]
[2,5,6,1,3,4] => [2,1,3,5,6,4]
[2,5,6,1,4,3] => [5,2,1,6,4,3]
[2,5,6,3,1,4] => [2,5,3,6,1,4]
[2,5,6,3,4,1] => [2,5,3,6,4,1]
[2,5,6,4,1,3] => [2,5,1,6,4,3]
[2,5,6,4,3,1] => [5,6,2,4,3,1]
[2,6,1,3,4,5] => [2,1,3,4,6,5]
[2,6,1,3,5,4] => [6,2,1,3,5,4]
[2,6,1,4,3,5] => [2,6,1,4,3,5]
[2,6,1,4,5,3] => [4,2,1,6,5,3]
[2,6,1,5,3,4] => [2,6,1,3,5,4]
[2,6,1,5,4,3] => [6,5,2,1,4,3]
[2,6,3,1,4,5] => [2,3,6,1,4,5]
[2,6,3,1,5,4] => [6,2,5,3,1,4]
[2,6,3,4,1,5] => [2,3,6,4,1,5]
[2,6,3,4,5,1] => [2,3,6,4,5,1]
[2,6,3,5,1,4] => [2,3,6,1,5,4]
[2,6,3,5,4,1] => [6,2,5,3,4,1]
[2,6,4,1,3,5] => [2,1,6,4,3,5]
[2,6,4,1,5,3] => [6,2,4,5,1,3]
[2,6,4,3,1,5] => [4,6,2,3,1,5]
[2,6,4,3,5,1] => [4,6,2,3,5,1]
[2,6,4,5,1,3] => [2,1,6,4,5,3]
[2,6,4,5,3,1] => [6,2,4,5,3,1]
[2,6,5,1,3,4] => [2,1,6,3,5,4]
[2,6,5,1,4,3] => [6,2,5,1,4,3]
[2,6,5,3,1,4] => [2,6,5,3,1,4]
[2,6,5,3,4,1] => [2,6,5,3,4,1]
[2,6,5,4,1,3] => [2,6,5,1,4,3]
[2,6,5,4,3,1] => [6,5,4,2,3,1]
[3,1,2,4,5,6] => [1,3,2,4,5,6]
[3,1,2,4,6,5] => [6,1,3,2,4,5]
[3,1,2,5,4,6] => [5,1,3,2,4,6]
[3,1,2,5,6,4] => [5,1,3,2,6,4]
[3,1,2,6,4,5] => [1,6,3,2,4,5]
[3,1,2,6,5,4] => [6,5,1,3,2,4]
[3,1,4,2,5,6] => [3,4,1,2,5,6]
[3,1,4,2,6,5] => [6,3,4,1,2,5]
[3,1,4,5,2,6] => [3,4,1,5,2,6]
[3,1,4,5,6,2] => [3,4,1,5,6,2]
[3,1,4,6,2,5] => [3,4,1,2,6,5]
[3,1,4,6,5,2] => [6,3,4,1,5,2]
[3,1,5,2,4,6] => [3,1,5,2,4,6]
[3,1,5,2,6,4] => [5,3,6,1,2,4]
[3,1,5,4,2,6] => [5,3,4,1,2,6]
[3,1,5,4,6,2] => [5,3,4,1,6,2]
[3,1,5,6,2,4] => [3,1,5,2,6,4]
[3,1,5,6,4,2] => [5,3,6,1,4,2]
[3,1,6,2,4,5] => [3,1,2,6,4,5]
[3,1,6,2,5,4] => [6,3,1,5,2,4]
[3,1,6,4,2,5] => [3,6,4,1,2,5]
[3,1,6,4,5,2] => [3,6,4,1,5,2]
[3,1,6,5,2,4] => [3,6,1,5,2,4]
[3,1,6,5,4,2] => [6,5,3,4,1,2]
[3,2,1,4,5,6] => [3,2,1,4,5,6]
[3,2,1,4,6,5] => [6,3,2,1,4,5]
[3,2,1,5,4,6] => [5,3,2,1,4,6]
[3,2,1,5,6,4] => [5,3,2,1,6,4]
[3,2,1,6,4,5] => [3,6,2,1,4,5]
[3,2,1,6,5,4] => [6,5,3,2,1,4]
[3,2,4,1,5,6] => [3,2,4,1,5,6]
[3,2,4,1,6,5] => [6,3,2,4,1,5]
[3,2,4,5,1,6] => [3,2,4,5,1,6]
[3,2,4,5,6,1] => [3,2,4,5,6,1]
[3,2,4,6,1,5] => [3,2,4,1,6,5]
[3,2,4,6,5,1] => [6,3,2,4,5,1]
[3,2,5,1,4,6] => [3,2,1,5,4,6]
[3,2,5,1,6,4] => [5,3,2,6,1,4]
[3,2,5,4,1,6] => [5,3,2,4,1,6]
[3,2,5,4,6,1] => [5,3,2,4,6,1]
[3,2,5,6,1,4] => [3,2,1,5,6,4]
[3,2,5,6,4,1] => [5,3,2,6,4,1]
[3,2,6,1,4,5] => [3,2,1,4,6,5]
[3,2,6,1,5,4] => [6,3,2,1,5,4]
[3,2,6,4,1,5] => [3,6,2,4,1,5]
[3,2,6,4,5,1] => [3,6,2,4,5,1]
[3,2,6,5,1,4] => [3,6,2,1,5,4]
[3,2,6,5,4,1] => [6,5,3,2,4,1]
[3,4,1,2,5,6] => [1,3,4,2,5,6]
[3,4,1,2,6,5] => [6,1,3,4,2,5]
[3,4,1,5,2,6] => [3,4,5,1,2,6]
[3,4,1,5,6,2] => [3,4,5,1,6,2]
[3,4,1,6,2,5] => [3,4,1,6,2,5]
[3,4,1,6,5,2] => [6,3,4,5,1,2]
[3,4,2,1,5,6] => [3,4,2,1,5,6]
[3,4,2,1,6,5] => [6,3,4,2,1,5]
[3,4,2,5,1,6] => [3,4,2,5,1,6]
[3,4,2,5,6,1] => [3,4,2,5,6,1]
[3,4,2,6,1,5] => [3,4,2,1,6,5]
[3,4,2,6,5,1] => [6,3,4,2,5,1]
[3,4,5,1,2,6] => [1,3,4,5,2,6]
[3,4,5,1,6,2] => [3,4,5,6,1,2]
[3,4,5,2,1,6] => [3,4,5,2,1,6]
[3,4,5,2,6,1] => [3,4,5,2,6,1]
[3,4,5,6,1,2] => [1,3,4,5,6,2]
[3,4,5,6,2,1] => [3,4,5,6,2,1]
[3,4,6,1,2,5] => [1,3,4,2,6,5]
[3,4,6,1,5,2] => [3,4,6,1,5,2]
[3,4,6,2,1,5] => [3,4,2,6,1,5]
[3,4,6,2,5,1] => [3,4,2,6,5,1]
[3,4,6,5,1,2] => [1,6,3,4,5,2]
[3,4,6,5,2,1] => [6,3,4,5,2,1]
[3,5,1,2,4,6] => [1,3,2,5,4,6]
[3,5,1,2,6,4] => [5,1,3,6,2,4]
[3,5,1,4,2,6] => [3,5,1,4,2,6]
[3,5,1,4,6,2] => [3,5,1,4,6,2]
[3,5,1,6,2,4] => [3,1,5,6,2,4]
[3,5,1,6,4,2] => [5,3,6,4,1,2]
[3,5,2,1,4,6] => [3,2,5,1,4,6]
[3,5,2,1,6,4] => [5,3,6,2,1,4]
[3,5,2,4,1,6] => [3,2,5,4,1,6]
[3,5,2,4,6,1] => [3,2,5,4,6,1]
[3,5,2,6,1,4] => [3,2,5,1,6,4]
[3,5,2,6,4,1] => [5,3,6,2,4,1]
[3,5,4,1,2,6] => [1,5,3,4,2,6]
[3,5,4,1,6,2] => [5,3,4,6,1,2]
[3,5,4,2,1,6] => [5,3,4,2,1,6]
[3,5,4,2,6,1] => [5,3,4,2,6,1]
[3,5,4,6,1,2] => [1,5,3,4,6,2]
[3,5,4,6,2,1] => [5,3,4,6,2,1]
[3,5,6,1,2,4] => [1,3,2,5,6,4]
[3,5,6,1,4,2] => [3,5,1,6,4,2]
[3,5,6,2,1,4] => [3,2,5,6,1,4]
[3,5,6,2,4,1] => [3,2,5,6,4,1]
[3,5,6,4,1,2] => [1,5,3,6,4,2]
[3,5,6,4,2,1] => [5,3,6,4,2,1]
[3,6,1,2,4,5] => [1,3,2,4,6,5]
[3,6,1,2,5,4] => [6,1,3,2,5,4]
[3,6,1,4,2,5] => [3,1,6,4,2,5]
[3,6,1,4,5,2] => [3,4,1,6,5,2]
[3,6,1,5,2,4] => [3,1,6,2,5,4]
[3,6,1,5,4,2] => [6,3,5,1,4,2]
[3,6,2,1,4,5] => [3,2,1,6,4,5]
[3,6,2,1,5,4] => [6,3,2,5,1,4]
[3,6,2,4,1,5] => [3,2,4,6,1,5]
[3,6,2,4,5,1] => [3,2,4,6,5,1]
[3,6,2,5,1,4] => [3,2,1,6,5,4]
[3,6,2,5,4,1] => [6,3,2,5,4,1]
[3,6,4,1,2,5] => [1,3,6,4,2,5]
[3,6,4,1,5,2] => [3,6,4,5,1,2]
[3,6,4,2,1,5] => [3,6,4,2,1,5]
[3,6,4,2,5,1] => [3,6,4,2,5,1]
[3,6,4,5,1,2] => [1,3,6,4,5,2]
[3,6,4,5,2,1] => [3,6,4,5,2,1]
[3,6,5,1,2,4] => [1,3,6,2,5,4]
[3,6,5,1,4,2] => [3,6,5,1,4,2]
[3,6,5,2,1,4] => [3,6,2,5,1,4]
[3,6,5,2,4,1] => [3,6,2,5,4,1]
[3,6,5,4,1,2] => [1,6,5,3,4,2]
[3,6,5,4,2,1] => [6,5,3,4,2,1]
[4,1,2,3,5,6] => [1,2,4,3,5,6]
[4,1,2,3,6,5] => [6,1,2,4,3,5]
[4,1,2,5,3,6] => [4,1,5,2,3,6]
[4,1,2,5,6,3] => [4,1,5,2,6,3]
[4,1,2,6,3,5] => [4,1,2,6,3,5]
[4,1,2,6,5,3] => [6,4,1,5,2,3]
[4,1,3,2,5,6] => [4,1,3,2,5,6]
[4,1,3,2,6,5] => [6,4,1,3,2,5]
[4,1,3,5,2,6] => [4,1,3,5,2,6]
[4,1,3,5,6,2] => [4,1,3,5,6,2]
[4,1,3,6,2,5] => [4,1,3,2,6,5]
[4,1,3,6,5,2] => [6,4,1,3,5,2]
[4,1,5,2,3,6] => [1,4,5,2,3,6]
[4,1,5,2,6,3] => [4,5,6,1,2,3]
[4,1,5,3,2,6] => [4,5,3,1,2,6]
[4,1,5,3,6,2] => [4,5,3,1,6,2]
[4,1,5,6,2,3] => [1,4,5,2,6,3]
[4,1,5,6,3,2] => [4,5,6,1,3,2]
[4,1,6,2,3,5] => [1,4,2,6,3,5]
[4,1,6,2,5,3] => [4,6,1,5,2,3]
[4,1,6,3,2,5] => [4,3,6,1,2,5]
[4,1,6,3,5,2] => [4,6,1,3,5,2]
[4,1,6,5,2,3] => [1,6,4,5,2,3]
[4,1,6,5,3,2] => [6,4,5,3,1,2]
[4,2,1,3,5,6] => [2,4,1,3,5,6]
[4,2,1,3,6,5] => [6,2,4,1,3,5]
[4,2,1,5,3,6] => [4,5,2,1,3,6]
[4,2,1,5,6,3] => [4,5,2,1,6,3]
[4,2,1,6,3,5] => [4,2,6,1,3,5]
[4,2,1,6,5,3] => [6,4,5,2,1,3]
[4,2,3,1,5,6] => [2,4,3,1,5,6]
[4,2,3,1,6,5] => [6,2,4,3,1,5]
[4,2,3,5,1,6] => [2,4,3,5,1,6]
[4,2,3,5,6,1] => [2,4,3,5,6,1]
[4,2,3,6,1,5] => [2,4,3,1,6,5]
[4,2,3,6,5,1] => [6,2,4,3,5,1]
[4,2,5,1,3,6] => [2,4,1,5,3,6]
[4,2,5,1,6,3] => [4,5,2,6,1,3]
[4,2,5,3,1,6] => [4,5,2,3,1,6]
[4,2,5,3,6,1] => [4,5,2,3,6,1]
[4,2,5,6,1,3] => [2,4,1,5,6,3]
[4,2,5,6,3,1] => [4,5,2,6,3,1]
[4,2,6,1,3,5] => [2,4,1,3,6,5]
[4,2,6,1,5,3] => [4,6,2,1,5,3]
[4,2,6,3,1,5] => [4,2,6,3,1,5]
[4,2,6,3,5,1] => [4,2,6,3,5,1]
[4,2,6,5,1,3] => [2,6,4,1,5,3]
[4,2,6,5,3,1] => [6,4,5,2,3,1]
[4,3,1,2,5,6] => [1,4,3,2,5,6]
[4,3,1,2,6,5] => [6,1,4,3,2,5]
[4,3,1,5,2,6] => [4,3,5,1,2,6]
[4,3,1,5,6,2] => [4,3,5,1,6,2]
[4,3,1,6,2,5] => [4,3,1,6,2,5]
[4,3,1,6,5,2] => [6,4,3,5,1,2]
[4,3,2,1,5,6] => [4,3,2,1,5,6]
[4,3,2,1,6,5] => [6,4,3,2,1,5]
[4,3,2,5,1,6] => [4,3,2,5,1,6]
[4,3,2,5,6,1] => [4,3,2,5,6,1]
[4,3,2,6,1,5] => [4,3,2,1,6,5]
[4,3,2,6,5,1] => [6,4,3,2,5,1]
[4,3,5,1,2,6] => [1,4,3,5,2,6]
[4,3,5,1,6,2] => [4,3,5,6,1,2]
[4,3,5,2,1,6] => [4,3,5,2,1,6]
[4,3,5,2,6,1] => [4,3,5,2,6,1]
[4,3,5,6,1,2] => [1,4,3,5,6,2]
[4,3,5,6,2,1] => [4,3,5,6,2,1]
[4,3,6,1,2,5] => [1,4,3,2,6,5]
[4,3,6,1,5,2] => [4,3,6,1,5,2]
[4,3,6,2,1,5] => [4,3,2,6,1,5]
[4,3,6,2,5,1] => [4,3,2,6,5,1]
[4,3,6,5,1,2] => [1,6,4,3,5,2]
[4,3,6,5,2,1] => [6,4,3,5,2,1]
[4,5,1,2,3,6] => [1,2,4,5,3,6]
[4,5,1,2,6,3] => [4,1,5,6,2,3]
[4,5,1,3,2,6] => [4,1,5,3,2,6]
[4,5,1,3,6,2] => [4,1,5,3,6,2]
[4,5,1,6,2,3] => [1,4,5,6,2,3]
[4,5,1,6,3,2] => [4,5,6,3,1,2]
[4,5,2,1,3,6] => [2,4,5,1,3,6]
[4,5,2,1,6,3] => [4,5,6,2,1,3]
[4,5,2,3,1,6] => [2,4,5,3,1,6]
[4,5,2,3,6,1] => [2,4,5,3,6,1]
[4,5,2,6,1,3] => [2,4,5,1,6,3]
[4,5,2,6,3,1] => [4,5,6,2,3,1]
[4,5,3,1,2,6] => [1,4,5,3,2,6]
[4,5,3,1,6,2] => [4,5,3,6,1,2]
[4,5,3,2,1,6] => [4,5,3,2,1,6]
[4,5,3,2,6,1] => [4,5,3,2,6,1]
[4,5,3,6,1,2] => [1,4,5,3,6,2]
[4,5,3,6,2,1] => [4,5,3,6,2,1]
[4,5,6,1,2,3] => [1,2,4,5,6,3]
[4,5,6,1,3,2] => [4,1,5,6,3,2]
[4,5,6,2,1,3] => [2,4,5,6,1,3]
[4,5,6,2,3,1] => [2,4,5,6,3,1]
[4,5,6,3,1,2] => [1,4,5,6,3,2]
[4,5,6,3,2,1] => [4,5,6,3,2,1]
[4,6,1,2,3,5] => [1,2,4,3,6,5]
[4,6,1,2,5,3] => [4,1,6,2,5,3]
[4,6,1,3,2,5] => [4,1,3,6,2,5]
[4,6,1,3,5,2] => [4,1,3,6,5,2]
[4,6,1,5,2,3] => [1,4,6,2,5,3]
[4,6,1,5,3,2] => [4,6,5,1,3,2]
[4,6,2,1,3,5] => [2,4,1,6,3,5]
[4,6,2,1,5,3] => [4,6,2,5,1,3]
[4,6,2,3,1,5] => [2,4,3,6,1,5]
[4,6,2,3,5,1] => [2,4,3,6,5,1]
[4,6,2,5,1,3] => [2,4,1,6,5,3]
[4,6,2,5,3,1] => [4,6,2,5,3,1]
[4,6,3,1,2,5] => [1,4,3,6,2,5]
[4,6,3,1,5,2] => [4,3,6,5,1,2]
[4,6,3,2,1,5] => [4,3,6,2,1,5]
[4,6,3,2,5,1] => [4,3,6,2,5,1]
[4,6,3,5,1,2] => [1,4,3,6,5,2]
[4,6,3,5,2,1] => [4,3,6,5,2,1]
[4,6,5,1,2,3] => [1,2,6,4,5,3]
[4,6,5,1,3,2] => [6,1,4,5,3,2]
[4,6,5,2,1,3] => [2,6,4,5,1,3]
[4,6,5,2,3,1] => [2,6,4,5,3,1]
[4,6,5,3,1,2] => [1,6,4,5,3,2]
[4,6,5,3,2,1] => [6,4,5,3,2,1]
[5,1,2,3,4,6] => [1,2,3,5,4,6]
[5,1,2,3,6,4] => [5,1,2,6,3,4]
[5,1,2,4,3,6] => [5,1,2,4,3,6]
[5,1,2,4,6,3] => [5,1,2,4,6,3]
[5,1,2,6,3,4] => [1,5,2,6,3,4]
[5,1,2,6,4,3] => [5,6,1,4,2,3]
[5,1,3,2,4,6] => [1,5,3,2,4,6]
[5,1,3,2,6,4] => [5,6,1,3,2,4]
[5,1,3,4,2,6] => [3,1,5,4,2,6]
[5,1,3,4,6,2] => [3,1,5,4,6,2]
[5,1,3,6,2,4] => [1,5,3,2,6,4]
[5,1,3,6,4,2] => [5,6,1,3,4,2]
[5,1,4,2,3,6] => [1,5,2,4,3,6]
[5,1,4,2,6,3] => [5,4,1,6,2,3]
[5,1,4,3,2,6] => [5,4,1,3,2,6]
[5,1,4,3,6,2] => [5,4,1,3,6,2]
[5,1,4,6,2,3] => [1,5,2,4,6,3]
[5,1,4,6,3,2] => [5,4,1,6,3,2]
[5,1,6,2,3,4] => [1,2,5,6,3,4]
[5,1,6,2,4,3] => [5,1,6,4,2,3]
[5,1,6,3,2,4] => [3,5,6,1,2,4]
[5,1,6,3,4,2] => [5,1,6,3,4,2]
[5,1,6,4,2,3] => [1,5,6,4,2,3]
[5,1,6,4,3,2] => [5,6,4,3,1,2]
[5,2,1,3,4,6] => [2,1,5,3,4,6]
[5,2,1,3,6,4] => [5,2,6,1,3,4]
[5,2,1,4,3,6] => [5,2,4,1,3,6]
[5,2,1,4,6,3] => [5,2,4,1,6,3]
[5,2,1,6,3,4] => [2,5,6,1,3,4]
[5,2,1,6,4,3] => [5,6,4,2,1,3]
[5,2,3,1,4,6] => [2,3,5,1,4,6]
[5,2,3,1,6,4] => [5,2,6,3,1,4]
[5,2,3,4,1,6] => [2,3,5,4,1,6]
[5,2,3,4,6,1] => [2,3,5,4,6,1]
[5,2,3,6,1,4] => [2,3,5,1,6,4]
[5,2,3,6,4,1] => [5,2,6,3,4,1]
[5,2,4,1,3,6] => [2,1,5,4,3,6]
[5,2,4,1,6,3] => [5,2,4,6,1,3]
[5,2,4,3,1,6] => [5,2,4,3,1,6]
[5,2,4,3,6,1] => [5,2,4,3,6,1]
[5,2,4,6,1,3] => [2,1,5,4,6,3]
[5,2,4,6,3,1] => [5,2,4,6,3,1]
[5,2,6,1,3,4] => [2,1,5,3,6,4]
[5,2,6,1,4,3] => [5,2,6,1,4,3]
[5,2,6,3,1,4] => [2,5,6,3,1,4]
[5,2,6,3,4,1] => [2,5,6,3,4,1]
[5,2,6,4,1,3] => [2,5,6,1,4,3]
[5,2,6,4,3,1] => [5,6,4,2,3,1]
[5,3,1,2,4,6] => [1,3,5,2,4,6]
[5,3,1,2,6,4] => [5,1,6,3,2,4]
[5,3,1,4,2,6] => [3,5,4,1,2,6]
[5,3,1,4,6,2] => [3,5,4,1,6,2]
[5,3,1,6,2,4] => [3,5,1,6,2,4]
[5,3,1,6,4,2] => [5,6,3,4,1,2]
[5,3,2,1,4,6] => [3,5,2,1,4,6]
[5,3,2,1,6,4] => [5,6,3,2,1,4]
[5,3,2,4,1,6] => [3,5,2,4,1,6]
[5,3,2,4,6,1] => [3,5,2,4,6,1]
[5,3,2,6,1,4] => [3,5,2,1,6,4]
[5,3,2,6,4,1] => [5,6,3,2,4,1]
[5,3,4,1,2,6] => [1,3,5,4,2,6]
[5,3,4,1,6,2] => [3,5,4,6,1,2]
[5,3,4,2,1,6] => [3,5,4,2,1,6]
[5,3,4,2,6,1] => [3,5,4,2,6,1]
[5,3,4,6,1,2] => [1,3,5,4,6,2]
[5,3,4,6,2,1] => [3,5,4,6,2,1]
[5,3,6,1,2,4] => [1,3,5,2,6,4]
[5,3,6,1,4,2] => [3,5,6,1,4,2]
[5,3,6,2,1,4] => [3,5,2,6,1,4]
[5,3,6,2,4,1] => [3,5,2,6,4,1]
[5,3,6,4,1,2] => [1,5,6,3,4,2]
[5,3,6,4,2,1] => [5,6,3,4,2,1]
[5,4,1,2,3,6] => [1,2,5,4,3,6]
[5,4,1,2,6,3] => [5,1,4,6,2,3]
[5,4,1,3,2,6] => [5,1,4,3,2,6]
[5,4,1,3,6,2] => [5,1,4,3,6,2]
[5,4,1,6,2,3] => [1,5,4,6,2,3]
[5,4,1,6,3,2] => [5,4,6,3,1,2]
[5,4,2,1,3,6] => [2,5,4,1,3,6]
[5,4,2,1,6,3] => [5,4,6,2,1,3]
[5,4,2,3,1,6] => [2,5,4,3,1,6]
[5,4,2,3,6,1] => [2,5,4,3,6,1]
[5,4,2,6,1,3] => [2,5,4,1,6,3]
[5,4,2,6,3,1] => [5,4,6,2,3,1]
[5,4,3,1,2,6] => [1,5,4,3,2,6]
[5,4,3,1,6,2] => [5,4,3,6,1,2]
[5,4,3,2,1,6] => [5,4,3,2,1,6]
[5,4,3,2,6,1] => [5,4,3,2,6,1]
[5,4,3,6,1,2] => [1,5,4,3,6,2]
[5,4,3,6,2,1] => [5,4,3,6,2,1]
[5,4,6,1,2,3] => [1,2,5,4,6,3]
[5,4,6,1,3,2] => [5,1,4,6,3,2]
[5,4,6,2,1,3] => [2,5,4,6,1,3]
[5,4,6,2,3,1] => [2,5,4,6,3,1]
[5,4,6,3,1,2] => [1,5,4,6,3,2]
[5,4,6,3,2,1] => [5,4,6,3,2,1]
[5,6,1,2,3,4] => [1,2,3,5,6,4]
[5,6,1,2,4,3] => [5,1,2,6,4,3]
[5,6,1,3,2,4] => [1,5,3,6,2,4]
[5,6,1,3,4,2] => [3,1,5,6,4,2]
[5,6,1,4,2,3] => [1,5,2,6,4,3]
[5,6,1,4,3,2] => [5,6,1,4,3,2]
[5,6,2,1,3,4] => [2,1,5,6,3,4]
[5,6,2,1,4,3] => [5,2,6,4,1,3]
[5,6,2,3,1,4] => [2,3,5,6,1,4]
[5,6,2,3,4,1] => [2,3,5,6,4,1]
[5,6,2,4,1,3] => [2,1,5,6,4,3]
[5,6,2,4,3,1] => [5,2,6,4,3,1]
[5,6,3,1,2,4] => [1,3,5,6,2,4]
[5,6,3,1,4,2] => [3,5,6,4,1,2]
[5,6,3,2,1,4] => [3,5,6,2,1,4]
[5,6,3,2,4,1] => [3,5,6,2,4,1]
[5,6,3,4,1,2] => [1,3,5,6,4,2]
[5,6,3,4,2,1] => [3,5,6,4,2,1]
[5,6,4,1,2,3] => [1,2,5,6,4,3]
[5,6,4,1,3,2] => [5,1,6,4,3,2]
[5,6,4,2,1,3] => [2,5,6,4,1,3]
[5,6,4,2,3,1] => [2,5,6,4,3,1]
[5,6,4,3,1,2] => [1,5,6,4,3,2]
[5,6,4,3,2,1] => [5,6,4,3,2,1]
[6,1,2,3,4,5] => [1,2,3,4,6,5]
[6,1,2,3,5,4] => [6,1,2,3,5,4]
[6,1,2,4,3,5] => [1,6,2,4,3,5]
[6,1,2,4,5,3] => [4,1,2,6,5,3]
[6,1,2,5,3,4] => [1,6,2,3,5,4]
[6,1,2,5,4,3] => [6,5,1,2,4,3]
[6,1,3,2,4,5] => [1,3,6,2,4,5]
[6,1,3,2,5,4] => [6,1,5,3,2,4]
[6,1,3,4,2,5] => [3,1,4,6,2,5]
[6,1,3,4,5,2] => [3,1,4,6,5,2]
[6,1,3,5,2,4] => [3,1,2,6,5,4]
[6,1,3,5,4,2] => [6,3,1,5,4,2]
[6,1,4,2,3,5] => [1,2,6,4,3,5]
[6,1,4,2,5,3] => [6,1,4,5,2,3]
[6,1,4,3,2,5] => [4,6,1,3,2,5]
[6,1,4,3,5,2] => [6,1,4,3,5,2]
[6,1,4,5,2,3] => [1,4,2,6,5,3]
[6,1,4,5,3,2] => [4,6,1,5,3,2]
[6,1,5,2,3,4] => [1,2,6,3,5,4]
[6,1,5,2,4,3] => [6,1,5,2,4,3]
[6,1,5,3,2,4] => [1,6,5,3,2,4]
[6,1,5,3,4,2] => [6,1,3,5,4,2]
[6,1,5,4,2,3] => [1,6,5,2,4,3]
[6,1,5,4,3,2] => [6,5,4,1,3,2]
[6,2,1,3,4,5] => [2,1,3,6,4,5]
[6,2,1,3,5,4] => [6,2,1,5,3,4]
[6,2,1,4,3,5] => [2,6,4,1,3,5]
[6,2,1,4,5,3] => [6,2,1,4,5,3]
[6,2,1,5,3,4] => [2,6,1,5,3,4]
[6,2,1,5,4,3] => [6,5,2,4,1,3]
[6,2,3,1,4,5] => [2,3,1,6,4,5]
[6,2,3,1,5,4] => [6,2,3,5,1,4]
[6,2,3,4,1,5] => [2,3,4,6,1,5]
[6,2,3,4,5,1] => [2,3,4,6,5,1]
[6,2,3,5,1,4] => [2,3,1,6,5,4]
[6,2,3,5,4,1] => [6,2,3,5,4,1]
[6,2,4,1,3,5] => [2,1,4,6,3,5]
[6,2,4,1,5,3] => [4,2,6,5,1,3]
[6,2,4,3,1,5] => [2,6,4,3,1,5]
[6,2,4,3,5,1] => [2,6,4,3,5,1]
[6,2,4,5,1,3] => [2,1,4,6,5,3]
[6,2,4,5,3,1] => [4,2,6,5,3,1]
[6,2,5,1,3,4] => [2,1,3,6,5,4]
[6,2,5,1,4,3] => [6,2,1,5,4,3]
[6,2,5,3,1,4] => [2,6,3,5,1,4]
[6,2,5,3,4,1] => [2,6,3,5,4,1]
[6,2,5,4,1,3] => [2,6,1,5,4,3]
[6,2,5,4,3,1] => [6,5,2,4,3,1]
[6,3,1,2,4,5] => [1,3,2,6,4,5]
[6,3,1,2,5,4] => [6,1,3,5,2,4]
[6,3,1,4,2,5] => [3,4,6,1,2,5]
[6,3,1,4,5,2] => [3,6,1,4,5,2]
[6,3,1,5,2,4] => [3,1,6,5,2,4]
[6,3,1,5,4,2] => [6,3,5,4,1,2]
[6,3,2,1,4,5] => [3,2,6,1,4,5]
[6,3,2,1,5,4] => [6,3,5,2,1,4]
[6,3,2,4,1,5] => [3,2,6,4,1,5]
[6,3,2,4,5,1] => [3,2,6,4,5,1]
[6,3,2,5,1,4] => [3,2,6,1,5,4]
[6,3,2,5,4,1] => [6,3,5,2,4,1]
[6,3,4,1,2,5] => [1,3,4,6,2,5]
[6,3,4,1,5,2] => [3,4,6,5,1,2]
[6,3,4,2,1,5] => [3,4,6,2,1,5]
[6,3,4,2,5,1] => [3,4,6,2,5,1]
[6,3,4,5,1,2] => [1,3,4,6,5,2]
[6,3,4,5,2,1] => [3,4,6,5,2,1]
[6,3,5,1,2,4] => [1,3,2,6,5,4]
[6,3,5,1,4,2] => [3,6,1,5,4,2]
[6,3,5,2,1,4] => [3,2,6,5,1,4]
[6,3,5,2,4,1] => [3,2,6,5,4,1]
[6,3,5,4,1,2] => [1,6,3,5,4,2]
[6,3,5,4,2,1] => [6,3,5,4,2,1]
[6,4,1,2,3,5] => [1,2,4,6,3,5]
[6,4,1,2,5,3] => [4,1,6,5,2,3]
[6,4,1,3,2,5] => [1,6,4,3,2,5]
[6,4,1,3,5,2] => [4,1,6,3,5,2]
[6,4,1,5,2,3] => [1,4,6,5,2,3]
[6,4,1,5,3,2] => [4,6,5,3,1,2]
[6,4,2,1,3,5] => [2,4,6,1,3,5]
[6,4,2,1,5,3] => [4,6,5,2,1,3]
[6,4,2,3,1,5] => [2,4,6,3,1,5]
[6,4,2,3,5,1] => [2,4,6,3,5,1]
[6,4,2,5,1,3] => [2,4,6,1,5,3]
[6,4,2,5,3,1] => [4,6,5,2,3,1]
[6,4,3,1,2,5] => [1,4,6,3,2,5]
[6,4,3,1,5,2] => [4,6,3,5,1,2]
[6,4,3,2,1,5] => [4,6,3,2,1,5]
[6,4,3,2,5,1] => [4,6,3,2,5,1]
[6,4,3,5,1,2] => [1,4,6,3,5,2]
[6,4,3,5,2,1] => [4,6,3,5,2,1]
[6,4,5,1,2,3] => [1,2,4,6,5,3]
[6,4,5,1,3,2] => [4,1,6,5,3,2]
[6,4,5,2,1,3] => [2,4,6,5,1,3]
[6,4,5,2,3,1] => [2,4,6,5,3,1]
[6,4,5,3,1,2] => [1,4,6,5,3,2]
[6,4,5,3,2,1] => [4,6,5,3,2,1]
[6,5,1,2,3,4] => [1,2,3,6,5,4]
[6,5,1,2,4,3] => [6,1,2,5,4,3]
[6,5,1,3,2,4] => [1,6,3,5,2,4]
[6,5,1,3,4,2] => [3,1,6,5,4,2]
[6,5,1,4,2,3] => [1,6,2,5,4,3]
[6,5,1,4,3,2] => [6,5,1,4,3,2]
[6,5,2,1,3,4] => [2,1,6,5,3,4]
[6,5,2,1,4,3] => [6,2,5,4,1,3]
[6,5,2,3,1,4] => [2,3,6,5,1,4]
[6,5,2,3,4,1] => [2,3,6,5,4,1]
[6,5,2,4,1,3] => [2,1,6,5,4,3]
[6,5,2,4,3,1] => [6,2,5,4,3,1]
[6,5,3,1,2,4] => [1,3,6,5,2,4]
[6,5,3,1,4,2] => [3,6,5,4,1,2]
[6,5,3,2,1,4] => [3,6,5,2,1,4]
[6,5,3,2,4,1] => [3,6,5,2,4,1]
[6,5,3,4,1,2] => [1,3,6,5,4,2]
[6,5,3,4,2,1] => [3,6,5,4,2,1]
[6,5,4,1,2,3] => [1,2,6,5,4,3]
[6,5,4,1,3,2] => [6,1,5,4,3,2]
[6,5,4,2,1,3] => [2,6,5,4,1,3]
[6,5,4,2,3,1] => [2,6,5,4,3,1]
[6,5,4,3,1,2] => [1,6,5,4,3,2]
[6,5,4,3,2,1] => [6,5,4,3,2,1]
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[1,2,3,4,5,7,6] => [7,1,2,3,4,5,6]
[1,2,3,4,6,5,7] => [6,1,2,3,4,5,7]
[1,2,3,4,6,7,5] => [6,1,2,3,4,7,5]
[1,2,3,4,7,5,6] => [1,7,2,3,4,5,6]
[1,2,3,4,7,6,5] => [7,6,1,2,3,4,5]
[1,2,3,5,4,6,7] => [5,1,2,3,4,6,7]
[1,2,3,5,4,7,6] => [7,5,1,2,3,4,6]
[1,2,3,5,6,4,7] => [5,1,2,3,6,4,7]
[1,2,3,5,6,7,4] => [5,1,2,3,6,7,4]
[1,2,3,5,7,4,6] => [5,1,2,3,4,7,6]
[1,2,3,5,7,6,4] => [7,5,1,2,3,6,4]
[1,2,3,6,4,5,7] => [1,6,2,3,4,5,7]
[1,2,3,6,4,7,5] => [6,7,1,2,3,4,5]
[1,2,3,6,5,4,7] => [6,5,1,2,3,4,7]
[1,2,3,6,5,7,4] => [6,5,1,2,3,7,4]
[1,2,3,6,7,4,5] => [1,6,2,3,4,7,5]
[1,2,3,6,7,5,4] => [6,7,1,2,3,5,4]
[1,2,3,7,4,5,6] => [1,2,7,3,4,5,6]
[1,2,3,7,4,6,5] => [7,1,6,2,3,4,5]
[1,2,3,7,5,4,6] => [5,7,1,2,3,4,6]
[1,2,3,7,5,6,4] => [7,1,5,2,3,6,4]
[1,2,3,7,6,4,5] => [1,7,6,2,3,4,5]
[1,2,3,7,6,5,4] => [7,6,5,1,2,3,4]
[1,2,4,3,5,6,7] => [4,1,2,3,5,6,7]
[1,2,4,3,5,7,6] => [7,4,1,2,3,5,6]
[1,2,4,3,6,5,7] => [6,4,1,2,3,5,7]
[1,2,4,3,6,7,5] => [6,4,1,2,3,7,5]
[1,2,4,3,7,5,6] => [4,7,1,2,3,5,6]
[1,2,4,3,7,6,5] => [7,6,4,1,2,3,5]
[1,2,4,5,3,6,7] => [4,1,2,5,3,6,7]
[1,2,4,5,3,7,6] => [7,4,1,2,5,3,6]
[1,2,4,5,6,3,7] => [4,1,2,5,6,3,7]
[1,2,4,5,6,7,3] => [4,1,2,5,6,7,3]
[1,2,4,5,7,3,6] => [4,1,2,5,3,7,6]
[1,2,4,5,7,6,3] => [7,4,1,2,5,6,3]
[1,2,4,6,3,5,7] => [4,1,2,3,6,5,7]
[1,2,4,6,3,7,5] => [6,4,1,2,7,3,5]
[1,2,4,6,5,3,7] => [6,4,1,2,5,3,7]
[1,2,4,6,5,7,3] => [6,4,1,2,5,7,3]
[1,2,4,6,7,3,5] => [4,1,2,3,6,7,5]
[1,2,4,6,7,5,3] => [6,4,1,2,7,5,3]
[1,2,4,7,3,5,6] => [4,1,2,3,5,7,6]
[1,2,4,7,3,6,5] => [7,4,1,2,3,6,5]
[1,2,4,7,5,3,6] => [4,7,1,2,5,3,6]
[1,2,4,7,5,6,3] => [7,1,4,2,5,6,3]
[1,2,4,7,6,3,5] => [4,7,1,2,3,6,5]
[1,2,4,7,6,5,3] => [7,6,4,1,2,5,3]
[1,2,5,3,4,6,7] => [1,5,2,3,4,6,7]
[1,2,5,3,4,7,6] => [7,1,5,2,3,4,6]
[1,2,5,3,6,4,7] => [5,6,1,2,3,4,7]
[1,2,5,3,6,7,4] => [5,6,1,2,3,7,4]
[1,2,5,3,7,4,6] => [5,1,7,2,3,4,6]
[1,2,5,3,7,6,4] => [7,5,6,1,2,3,4]
[1,2,5,4,3,6,7] => [5,4,1,2,3,6,7]
[1,2,5,4,3,7,6] => [7,5,4,1,2,3,6]
[1,2,5,4,6,3,7] => [5,4,1,2,6,3,7]
[1,2,5,4,6,7,3] => [5,4,1,2,6,7,3]
[1,2,5,4,7,3,6] => [5,4,1,2,3,7,6]
[1,2,5,4,7,6,3] => [7,5,4,1,2,6,3]
[1,2,5,6,3,4,7] => [1,5,2,3,6,4,7]
[1,2,5,6,3,7,4] => [5,6,1,2,7,3,4]
[1,2,5,6,4,3,7] => [5,6,1,2,4,3,7]
[1,2,5,6,4,7,3] => [5,6,1,2,4,7,3]
[1,2,5,6,7,3,4] => [1,5,2,3,6,7,4]
[1,2,5,6,7,4,3] => [5,6,1,2,7,4,3]
[1,2,5,7,3,4,6] => [1,5,2,3,4,7,6]
[1,2,5,7,3,6,4] => [5,7,1,2,3,6,4]
[1,2,5,7,4,3,6] => [5,1,7,2,4,3,6]
[1,2,5,7,4,6,3] => [5,4,1,2,7,6,3]
[1,2,5,7,6,3,4] => [1,7,5,2,3,6,4]
[1,2,5,7,6,4,3] => [7,5,6,1,2,4,3]
[1,2,6,3,4,5,7] => [1,2,6,3,4,5,7]
[1,2,6,3,4,7,5] => [6,1,7,2,3,4,5]
[1,2,6,3,5,4,7] => [6,1,5,2,3,4,7]
[1,2,6,3,5,7,4] => [6,1,5,2,3,7,4]
[1,2,6,3,7,4,5] => [1,6,7,2,3,4,5]
[1,2,6,3,7,5,4] => [6,7,5,1,2,3,4]
[1,2,6,4,3,5,7] => [4,6,1,2,3,5,7]
[1,2,6,4,3,7,5] => [6,7,4,1,2,3,5]
[1,2,6,4,5,3,7] => [6,1,4,2,5,3,7]
[1,2,6,4,5,7,3] => [6,1,4,2,5,7,3]
[1,2,6,4,7,3,5] => [4,6,1,2,3,7,5]
[1,2,6,4,7,5,3] => [6,7,4,1,2,5,3]
[1,2,6,5,3,4,7] => [1,6,5,2,3,4,7]
[1,2,6,5,3,7,4] => [6,5,7,1,2,3,4]
[1,2,6,5,4,3,7] => [6,5,4,1,2,3,7]
[1,2,6,5,4,7,3] => [6,5,4,1,2,7,3]
[1,2,6,5,7,3,4] => [1,6,5,2,3,7,4]
[1,2,6,5,7,4,3] => [6,5,7,1,2,4,3]
[1,2,6,7,3,4,5] => [1,2,6,3,4,7,5]
[1,2,6,7,3,5,4] => [6,1,7,2,3,5,4]
[1,2,6,7,4,3,5] => [1,6,7,2,4,3,5]
[1,2,6,7,4,5,3] => [6,1,4,2,7,5,3]
[1,2,6,7,5,3,4] => [1,6,7,2,3,5,4]
[1,2,6,7,5,4,3] => [6,7,5,1,2,4,3]
[1,2,7,3,4,5,6] => [1,2,3,7,4,5,6]
[1,2,7,3,4,6,5] => [7,1,2,6,3,4,5]
[1,2,7,3,5,4,6] => [1,7,5,2,3,4,6]
[1,2,7,3,5,6,4] => [7,1,2,5,3,6,4]
[1,2,7,3,6,4,5] => [1,7,2,6,3,4,5]
[1,2,7,3,6,5,4] => [7,6,1,5,2,3,4]
[1,2,7,4,3,5,6] => [4,1,7,2,3,5,6]
[1,2,7,4,3,6,5] => [7,4,6,1,2,3,5]
[1,2,7,4,5,3,6] => [1,7,4,2,5,3,6]
[1,2,7,4,5,6,3] => [7,1,2,4,5,6,3]
[1,2,7,4,6,3,5] => [1,7,4,2,3,6,5]
[1,2,7,4,6,5,3] => [7,6,1,4,2,5,3]
[1,2,7,5,3,4,6] => [1,5,7,2,3,4,6]
[1,2,7,5,3,6,4] => [5,7,6,1,2,3,4]
[1,2,7,5,4,3,6] => [5,7,4,1,2,3,6]
[1,2,7,5,4,6,3] => [5,7,4,1,2,6,3]
[1,2,7,5,6,3,4] => [1,7,2,5,3,6,4]
[1,2,7,5,6,4,3] => [7,5,1,6,2,4,3]
[1,2,7,6,3,4,5] => [1,2,7,6,3,4,5]
[1,2,7,6,3,5,4] => [7,1,6,5,2,3,4]
[1,2,7,6,4,3,5] => [4,7,6,1,2,3,5]
[1,2,7,6,4,5,3] => [7,1,6,4,2,5,3]
[1,2,7,6,5,3,4] => [1,7,6,5,2,3,4]
[1,2,7,6,5,4,3] => [7,6,5,4,1,2,3]
[1,3,2,4,5,6,7] => [3,1,2,4,5,6,7]
[1,3,2,4,5,7,6] => [7,3,1,2,4,5,6]
[1,3,2,4,6,5,7] => [6,3,1,2,4,5,7]
[1,3,2,4,6,7,5] => [6,3,1,2,4,7,5]
[1,3,2,4,7,5,6] => [3,7,1,2,4,5,6]
[1,3,2,4,7,6,5] => [7,6,3,1,2,4,5]
[1,3,2,5,4,6,7] => [5,3,1,2,4,6,7]
[1,3,2,5,4,7,6] => [7,5,3,1,2,4,6]
[1,3,2,5,6,4,7] => [5,3,1,2,6,4,7]
[1,3,2,5,6,7,4] => [5,3,1,2,6,7,4]
[1,3,2,5,7,4,6] => [5,3,1,2,4,7,6]
[1,3,2,5,7,6,4] => [7,5,3,1,2,6,4]
[1,3,2,6,4,5,7] => [3,6,1,2,4,5,7]
[1,3,2,6,4,7,5] => [6,7,3,1,2,4,5]
[1,3,2,6,5,4,7] => [6,5,3,1,2,4,7]
[1,3,2,6,5,7,4] => [6,5,3,1,2,7,4]
[1,3,2,6,7,4,5] => [3,6,1,2,4,7,5]
[1,3,2,6,7,5,4] => [6,7,3,1,2,5,4]
[1,3,2,7,4,5,6] => [3,1,7,2,4,5,6]
[1,3,2,7,4,6,5] => [7,3,6,1,2,4,5]
[1,3,2,7,5,4,6] => [5,7,3,1,2,4,6]
[1,3,2,7,5,6,4] => [7,3,5,1,2,6,4]
[1,3,2,7,6,4,5] => [3,7,6,1,2,4,5]
[1,3,2,7,6,5,4] => [7,6,5,3,1,2,4]
[1,3,4,2,5,6,7] => [3,1,4,2,5,6,7]
[1,3,4,2,5,7,6] => [7,3,1,4,2,5,6]
[1,3,4,2,6,5,7] => [6,3,1,4,2,5,7]
[1,3,4,2,6,7,5] => [6,3,1,4,2,7,5]
[1,3,4,2,7,5,6] => [3,7,1,4,2,5,6]
[1,3,4,2,7,6,5] => [7,6,3,1,4,2,5]
[1,3,4,5,2,6,7] => [3,1,4,5,2,6,7]
[1,3,4,5,2,7,6] => [7,3,1,4,5,2,6]
[1,3,4,5,6,2,7] => [3,1,4,5,6,2,7]
[1,3,4,5,6,7,2] => [3,1,4,5,6,7,2]
[1,3,4,5,7,2,6] => [3,1,4,5,2,7,6]
[1,3,4,5,7,6,2] => [7,3,1,4,5,6,2]
[1,3,4,6,2,5,7] => [3,1,4,2,6,5,7]
[1,3,4,6,2,7,5] => [6,3,1,4,7,2,5]
[1,3,4,6,5,2,7] => [6,3,1,4,5,2,7]
[1,3,4,6,5,7,2] => [6,3,1,4,5,7,2]
[1,3,4,6,7,2,5] => [3,1,4,2,6,7,5]
[1,3,4,6,7,5,2] => [6,3,1,4,7,5,2]
[1,3,4,7,2,5,6] => [3,1,4,2,5,7,6]
[1,3,4,7,2,6,5] => [7,3,1,4,2,6,5]
[1,3,4,7,5,2,6] => [3,7,1,4,5,2,6]
[1,3,4,7,5,6,2] => [7,1,3,4,5,6,2]
[1,3,4,7,6,2,5] => [3,7,1,4,2,6,5]
[1,3,4,7,6,5,2] => [7,6,3,1,4,5,2]
[1,3,5,2,4,6,7] => [3,1,2,5,4,6,7]
[1,3,5,2,4,7,6] => [7,3,1,2,5,4,6]
[1,3,5,2,6,4,7] => [5,3,1,6,2,4,7]
[1,3,5,2,6,7,4] => [5,3,1,6,2,7,4]
[1,3,5,2,7,4,6] => [5,3,1,2,7,4,6]
[1,3,5,2,7,6,4] => [7,5,3,1,6,2,4]
[1,3,5,4,2,6,7] => [5,3,1,4,2,6,7]
[1,3,5,4,2,7,6] => [7,5,3,1,4,2,6]
[1,3,5,4,6,2,7] => [5,3,1,4,6,2,7]
[1,3,5,4,6,7,2] => [5,3,1,4,6,7,2]
[1,3,5,4,7,2,6] => [5,3,1,4,2,7,6]
[1,3,5,4,7,6,2] => [7,5,3,1,4,6,2]
[1,3,5,6,2,4,7] => [3,1,2,5,6,4,7]
[1,3,5,6,2,7,4] => [5,3,1,6,7,2,4]
[1,3,5,6,4,2,7] => [5,3,1,6,4,2,7]
[1,3,5,6,4,7,2] => [5,3,1,6,4,7,2]
[1,3,5,6,7,2,4] => [3,1,2,5,6,7,4]
[1,3,5,6,7,4,2] => [5,3,1,6,7,4,2]
[1,3,5,7,2,4,6] => [3,1,2,5,4,7,6]
[1,3,5,7,2,6,4] => [5,3,1,7,2,6,4]
[1,3,5,7,4,2,6] => [5,3,1,4,7,2,6]
[1,3,5,7,4,6,2] => [5,3,1,4,7,6,2]
[1,3,5,7,6,2,4] => [3,7,1,2,5,6,4]
[1,3,5,7,6,4,2] => [7,5,3,1,6,4,2]
[1,3,6,2,4,5,7] => [3,1,2,4,6,5,7]
[1,3,6,2,4,7,5] => [6,3,1,2,7,4,5]
[1,3,6,2,5,4,7] => [6,3,1,2,5,4,7]
[1,3,6,2,5,7,4] => [6,3,1,2,5,7,4]
[1,3,6,2,7,4,5] => [3,6,1,2,7,4,5]
[1,3,6,2,7,5,4] => [6,7,3,1,5,2,4]
[1,3,6,4,2,5,7] => [3,6,1,4,2,5,7]
[1,3,6,4,2,7,5] => [6,7,3,1,4,2,5]
[1,3,6,4,5,2,7] => [6,1,3,4,5,2,7]
[1,3,6,4,5,7,2] => [6,1,3,4,5,7,2]
[1,3,6,4,7,2,5] => [3,6,1,4,2,7,5]
[1,3,6,4,7,5,2] => [6,7,3,1,4,5,2]
[1,3,6,5,2,4,7] => [3,6,1,2,5,4,7]
[1,3,6,5,2,7,4] => [6,5,3,1,7,2,4]
[1,3,6,5,4,2,7] => [6,5,3,1,4,2,7]
[1,3,6,5,4,7,2] => [6,5,3,1,4,7,2]
[1,3,6,5,7,2,4] => [3,6,1,2,5,7,4]
[1,3,6,5,7,4,2] => [6,5,3,1,7,4,2]
[1,3,6,7,2,4,5] => [3,1,2,4,6,7,5]
[1,3,6,7,2,5,4] => [6,3,1,2,7,5,4]
[1,3,6,7,4,2,5] => [3,6,1,4,7,2,5]
[1,3,6,7,4,5,2] => [6,1,3,4,7,5,2]
[1,3,6,7,5,2,4] => [3,6,1,2,7,5,4]
[1,3,6,7,5,4,2] => [6,7,3,1,5,4,2]
[1,3,7,2,4,5,6] => [3,1,2,4,5,7,6]
[1,3,7,2,4,6,5] => [7,3,1,2,4,6,5]
[1,3,7,2,5,4,6] => [3,7,1,2,5,4,6]
[1,3,7,2,5,6,4] => [5,3,1,2,7,6,4]
[1,3,7,2,6,4,5] => [3,7,1,2,4,6,5]
[1,3,7,2,6,5,4] => [7,6,3,1,2,5,4]
[1,3,7,4,2,5,6] => [3,1,7,4,2,5,6]
[1,3,7,4,2,6,5] => [7,3,6,1,4,2,5]
[1,3,7,4,5,2,6] => [1,7,3,4,5,2,6]
[1,3,7,4,5,6,2] => [3,1,7,4,5,6,2]
[1,3,7,4,6,2,5] => [1,7,3,4,2,6,5]
[1,3,7,4,6,5,2] => [7,6,1,3,4,5,2]
[1,3,7,5,2,4,6] => [3,1,7,2,5,4,6]
[1,3,7,5,2,6,4] => [7,3,5,1,6,2,4]
[1,3,7,5,4,2,6] => [5,7,3,1,4,2,6]
[1,3,7,5,4,6,2] => [5,7,3,1,4,6,2]
[1,3,7,5,6,2,4] => [1,7,3,2,5,6,4]
[1,3,7,5,6,4,2] => [7,5,1,3,6,4,2]
[1,3,7,6,2,4,5] => [3,1,7,2,4,6,5]
[1,3,7,6,2,5,4] => [7,3,6,1,2,5,4]
[1,3,7,6,4,2,5] => [3,7,6,1,4,2,5]
[1,3,7,6,4,5,2] => [7,1,6,3,4,5,2]
[1,3,7,6,5,2,4] => [3,7,6,1,2,5,4]
[1,3,7,6,5,4,2] => [7,6,5,3,1,4,2]
[1,4,2,3,5,6,7] => [1,4,2,3,5,6,7]
[1,4,2,3,5,7,6] => [7,1,4,2,3,5,6]
[1,4,2,3,6,5,7] => [6,1,4,2,3,5,7]
[1,4,2,3,6,7,5] => [6,1,4,2,3,7,5]
[1,4,2,3,7,5,6] => [1,7,4,2,3,5,6]
[1,4,2,3,7,6,5] => [7,6,1,4,2,3,5]
[1,4,2,5,3,6,7] => [4,5,1,2,3,6,7]
[1,4,2,5,3,7,6] => [7,4,5,1,2,3,6]
[1,4,2,5,6,3,7] => [4,5,1,2,6,3,7]
[1,4,2,5,6,7,3] => [4,5,1,2,6,7,3]
[1,4,2,5,7,3,6] => [4,5,1,2,3,7,6]
[1,4,2,5,7,6,3] => [7,4,5,1,2,6,3]
[1,4,2,6,3,5,7] => [4,1,6,2,3,5,7]
[1,4,2,6,3,7,5] => [6,4,7,1,2,3,5]
[1,4,2,6,5,3,7] => [6,4,5,1,2,3,7]
[1,4,2,6,5,7,3] => [6,4,5,1,2,7,3]
[1,4,2,6,7,3,5] => [4,1,6,2,3,7,5]
[1,4,2,6,7,5,3] => [6,4,7,1,2,5,3]
[1,4,2,7,3,5,6] => [4,1,2,7,3,5,6]
[1,4,2,7,3,6,5] => [7,4,1,6,2,3,5]
[1,4,2,7,5,3,6] => [4,7,5,1,2,3,6]
[1,4,2,7,5,6,3] => [4,7,5,1,2,6,3]
[1,4,2,7,6,3,5] => [4,7,1,6,2,3,5]
[1,4,2,7,6,5,3] => [7,6,4,5,1,2,3]
[1,4,3,2,5,6,7] => [4,3,1,2,5,6,7]
[1,4,3,2,5,7,6] => [7,4,3,1,2,5,6]
[1,4,3,2,6,5,7] => [6,4,3,1,2,5,7]
[1,4,3,2,6,7,5] => [6,4,3,1,2,7,5]
[1,4,3,2,7,5,6] => [4,7,3,1,2,5,6]
[1,4,3,2,7,6,5] => [7,6,4,3,1,2,5]
[1,4,3,5,2,6,7] => [4,3,1,5,2,6,7]
[1,4,3,5,2,7,6] => [7,4,3,1,5,2,6]
[1,4,3,5,6,2,7] => [4,3,1,5,6,2,7]
[1,4,3,5,6,7,2] => [4,3,1,5,6,7,2]
[1,4,3,5,7,2,6] => [4,3,1,5,2,7,6]
[1,4,3,5,7,6,2] => [7,4,3,1,5,6,2]
[1,4,3,6,2,5,7] => [4,3,1,2,6,5,7]
[1,4,3,6,2,7,5] => [6,4,3,1,7,2,5]
[1,4,3,6,5,2,7] => [6,4,3,1,5,2,7]
[1,4,3,6,5,7,2] => [6,4,3,1,5,7,2]
[1,4,3,6,7,2,5] => [4,3,1,2,6,7,5]
[1,4,3,6,7,5,2] => [6,4,3,1,7,5,2]
[1,4,3,7,2,5,6] => [4,3,1,2,5,7,6]
[1,4,3,7,2,6,5] => [7,4,3,1,2,6,5]
[1,4,3,7,5,2,6] => [4,7,3,1,5,2,6]
[1,4,3,7,5,6,2] => [4,7,3,1,5,6,2]
[1,4,3,7,6,2,5] => [4,7,3,1,2,6,5]
[1,4,3,7,6,5,2] => [7,6,4,3,1,5,2]
[1,4,5,2,3,6,7] => [1,4,2,5,3,6,7]
[1,4,5,2,3,7,6] => [7,1,4,2,5,3,6]
[1,4,5,2,6,3,7] => [4,5,1,6,2,3,7]
[1,4,5,2,6,7,3] => [4,5,1,6,2,7,3]
[1,4,5,2,7,3,6] => [4,5,1,2,7,3,6]
[1,4,5,2,7,6,3] => [7,4,5,1,6,2,3]
[1,4,5,3,2,6,7] => [4,5,1,3,2,6,7]
[1,4,5,3,2,7,6] => [7,4,5,1,3,2,6]
[1,4,5,3,6,2,7] => [4,5,1,3,6,2,7]
[1,4,5,3,6,7,2] => [4,5,1,3,6,7,2]
[1,4,5,3,7,2,6] => [4,5,1,3,2,7,6]
[1,4,5,3,7,6,2] => [7,4,5,1,3,6,2]
[1,4,5,6,2,3,7] => [1,4,2,5,6,3,7]
[1,4,5,6,2,7,3] => [4,5,1,6,7,2,3]
[1,4,5,6,3,2,7] => [4,5,1,6,3,2,7]
[1,4,5,6,3,7,2] => [4,5,1,6,3,7,2]
[1,4,5,6,7,2,3] => [1,4,2,5,6,7,3]
[1,4,5,6,7,3,2] => [4,5,1,6,7,3,2]
[1,4,5,7,2,3,6] => [1,4,2,5,3,7,6]
[1,4,5,7,2,6,3] => [4,5,1,7,2,6,3]
[1,4,5,7,3,2,6] => [4,5,1,3,7,2,6]
[1,4,5,7,3,6,2] => [4,5,1,3,7,6,2]
[1,4,5,7,6,2,3] => [1,7,4,2,5,6,3]
[1,4,5,7,6,3,2] => [7,4,5,1,6,3,2]
[1,4,6,2,3,5,7] => [1,4,2,3,6,5,7]
[1,4,6,2,3,7,5] => [6,1,4,2,7,3,5]
[1,4,6,2,5,3,7] => [4,6,1,2,5,3,7]
[1,4,6,2,5,7,3] => [4,6,1,2,5,7,3]
[1,4,6,2,7,3,5] => [4,1,6,2,7,3,5]
[1,4,6,2,7,5,3] => [6,4,7,1,5,2,3]
[1,4,6,3,2,5,7] => [4,1,6,3,2,5,7]
[1,4,6,3,2,7,5] => [6,4,7,1,3,2,5]
[1,4,6,3,5,2,7] => [4,3,1,6,5,2,7]
[1,4,6,3,5,7,2] => [4,3,1,6,5,7,2]
[1,4,6,3,7,2,5] => [4,1,6,3,2,7,5]
[1,4,6,3,7,5,2] => [6,4,7,1,3,5,2]
[1,4,6,5,2,3,7] => [1,6,4,2,5,3,7]
[1,4,6,5,2,7,3] => [6,4,5,1,7,2,3]
[1,4,6,5,3,2,7] => [6,4,5,1,3,2,7]
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Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Properties
bijectiveA map $\phi: A \rightarrow B$ is bijective if it is both injective and surjective. This is if (1) $\phi(a) = \phi(b)$ implies $a=b$, and (2) for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
References
[1] Foata, D., Schützenberger, M.-P. Major index and inversion number of permutations MathSciNet:0506852
[2] Mp00096Foata bijection
Code
def foata_bijection(elt):
    L = list(elt)
    M = []
    for e in L:
        M.append(e)
        k = len(M)
        if k <= 1:
            continue

        a = M[-2]
        M_prime = [0]*k
        if a > e:
            index_list = [-1] + [i for i in range(k - 1) if M[i] > e]
        else:
            index_list = [-1] + [i for i in range(k - 1) if M[i] < e]

        for j in range(1, len(index_list)):
            start = index_list[j-1] + 1
            end = index_list[j]
            M_prime[start] = M[end]
            for x in range(start + 1, end + 1):
                M_prime[x] = M[x-1]
        M_prime[k-1] = e
        M = M_prime
    return Permutations()(M)
Updated
May 16, 2019 at 07:57 by Christian Stump