Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
St001346: Permutations ⟶ ℤ
Values
[1,0,1,0] => [2,1] => 1
[1,1,0,0] => [1,2] => 2
[1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,1,0,0] => [2,3,1] => 2
[1,1,0,0,1,0] => [3,1,2] => 2
[1,1,0,1,0,0] => [2,1,3] => 3
[1,1,1,0,0,0] => [1,2,3] => 6
[1,0,1,0,1,0,1,0] => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0] => [3,4,2,1] => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 6
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 2
[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] => 3
[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] => 8
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 6
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 8
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 12
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 24
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 2
[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] => 6
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 2
[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] => 4
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 8
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 6
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 8
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 12
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 24
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 4
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 4
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 6
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 12
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 3
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 6
[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] => 5
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 10
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 8
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 10
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 15
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 30
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 6
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 12
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 8
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 10
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 20
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 12
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 15
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 20
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 40
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 24
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 30
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 40
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 60
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 120
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 8
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 8
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 12
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 24
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 2
[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] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 12
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 10
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 10
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 15
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 30
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 12
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 8
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 10
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 20
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 12
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 15
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 20
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 40
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 24
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Description
The number of parking functions that give the same permutation.
A parking function $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
A parking function $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
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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