Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
St000235: Permutations ⟶ ℤ
Values
[1,0] => [1] => 0
[1,0,1,0] => [2,1] => 0
[1,1,0,0] => [1,2] => 2
[1,0,1,0,1,0] => [3,2,1] => 2
[1,0,1,1,0,0] => [2,3,1] => 0
[1,1,0,0,1,0] => [3,1,2] => 3
[1,1,0,1,0,0] => [2,1,3] => 2
[1,1,1,0,0,0] => [1,2,3] => 3
[1,0,1,0,1,0,1,0] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => 3
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[1,1,0,0,1,1,0,0] => [3,4,1,2] => 4
[1,1,0,1,0,0,1,0] => [4,2,1,3] => 4
[1,1,0,1,0,1,0,0] => [3,2,1,4] => 4
[1,1,0,1,1,0,0,0] => [2,3,1,4] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 4
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 4
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 4
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 3
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 4
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 4
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 4
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 3
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 3
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 3
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 3
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 4
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 5
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 5
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 4
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 5
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 5
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 5
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 5
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 5
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 4
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 4
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 5
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 5
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 5
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 5
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 3
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 5
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 5
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 5
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [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] => 3
>>> Load all 196 entries. <<<
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Description
The number of indices that are not cyclical small weak excedances.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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