- FindStat

Identifier

Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000702: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 300 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{2} = q + q^{2}$

$F_{3} = q + 3\ q^{2} + q^{3}$

$F_{4} = q + 7\ q^{2} + 5\ q^{3} + q^{4}$

$F_{5} = q + 16\ q^{2} + 17\ q^{3} + 7\ q^{4} + q^{5}$

$F_{6} = q + 30\ q^{2} + 62\ q^{3} + 29\ q^{4} + 9\ q^{5} + q^{6}$

Description

The number of weak deficiencies of a permutation.
This is defined as

$\operatorname{wdec}(\sigma)=\#\{i:\sigma(i) \leq i\}.$
The number of weak exceedances is St000213The number of weak exceedances (also weak excedences) of a permutation., the number of deficiencies is St000703The number of deficiencies of a permutation..

Map

inverse

Description

Sends a permutation to its inverse.

Map

major-index to inversion-number bijection

Description

Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.

Map

to 132-avoiding permutation

Description

Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].