- FindStat

Identifier

Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
St001489: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 282 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 3\ q + q^{2}$

$F_{4} = 1 + 5\ q + 7\ q^{2} + q^{3}$

$F_{5} = 1 + 7\ q + 18\ q^{2} + 15\ q^{3} + q^{4}$

$F_{6} = 1 + 9\ q + 33\ q^{2} + 57\ q^{3} + 31\ q^{4} + q^{5}$

Description

The maximum of the number of descents and the number of inverse descents.
This is, the maximum of St000021The number of descents of a permutation. and St000354The number of recoils of a permutation..

Map

complement

Description

Sents a permutation to its complement.
The complement of a permutation

$\sigma$ of length

$n$ is the permutation

$\tau$ with

$\tau(i) = n+1-\sigma(i)$

Map

Clarke-Steingrimsson-Zeng inverse

Description

The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map

$\Phi$ in [1, sec.3].

Map

to 132-avoiding permutation

Description

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