- FindStat

Identifier

Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001498: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 127 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The normalised height of a Nakayama algebra with magnitude 1.
We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.

Map

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let

$(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are

$c_1, c_1+c_2, \dots, c_1+\dots+c_k$ .
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

Corteel

Description

Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.