Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000483
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00237: Permutations —descent views to invisible inversion bottoms⟶ Permutations
St000483: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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] => 0
[1,0,1,0,1,0]
 => [3,2,1] => [1,3,2] => [1,3,2] => 1
[1,0,1,1,0,0]
 => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0]
 => [3,1,2] => [3,1,2] => [3,1,2] => 1
[1,1,0,1,0,0]
 => [2,1,3] => [3,2,1] => [2,3,1] => 1
[1,1,1,0,0,0]
 => [1,2,3] => [2,3,1] => [3,2,1] => 0
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => [1,4,3,2] => [1,3,4,2] => 1
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => [1,3,4,2] => [1,4,3,2] => 1
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => [1,3,2,4] => [1,3,2,4] => 2
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => [4,1,3,2] => [4,3,1,2] => 1
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => [4,3,1,2] => [3,1,4,2] => 2
[1,1,0,1,0,1,0,0]
 => [3,2,1,4] => [4,3,2,1] => [2,3,4,1] => 1
[1,1,0,1,1,0,0,0]
 => [2,3,1,4] => [4,2,3,1] => [3,4,2,1] => 1
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [3,4,1,2] => [4,1,3,2] => 2
[1,1,1,0,0,1,0,0]
 => [3,1,2,4] => [3,4,2,1] => [2,4,3,1] => 1
[1,1,1,0,1,0,0,0]
 => [2,1,3,4] => [3,2,4,1] => [4,3,2,1] => 0
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [2,3,4,1] => [4,2,3,1] => 2
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => [1,5,4,3,2] => [1,3,4,5,2] => 1
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => [1,5,4,2,3] => [1,4,2,5,3] => 3
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => [1,5,3,4,2] => [1,4,5,3,2] => 1
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => [1,5,3,2,4] => [1,3,5,2,4] => 2
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => [1,4,5,3,2] => [1,3,5,4,2] => 1
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => [1,4,5,2,3] => [1,5,2,4,3] => 3
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => [1,4,3,5,2] => [1,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => [1,4,3,2,5] => [1,3,4,2,5] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => [1,3,4,5,2] => [1,5,3,4,2] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => [1,3,4,2,5] => [1,4,3,2,5] => 2
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => [5,1,4,3,2] => [5,3,4,1,2] => 3
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => [5,1,4,2,3] => [5,4,2,1,3] => 1
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => [5,1,3,4,2] => [5,4,1,3,2] => 2
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => [5,1,3,2,4] => [5,3,1,2,4] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [5,1,2,3,4] => [5,1,2,3,4] => 1
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => [5,4,1,3,2] => [4,3,1,5,2] => 2
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => [5,4,1,2,3] => [4,1,2,5,3] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => [5,4,3,1,2] => [3,1,4,5,2] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => [5,4,3,2,1] => [2,3,4,5,1] => 1
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => [5,4,2,3,1] => [3,4,2,5,1] => 3
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => [5,3,4,1,2] => [4,1,5,3,2] => 2
[1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => [5,3,4,2,1] => [2,4,5,3,1] => 1
[1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => [5,3,2,4,1] => [4,3,5,2,1] => 2
[1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => [5,2,3,4,1] => [4,5,2,3,1] => 3
Description
The number of times a permutation switches from increasing to decreasing or decreasing to increasing. This is the same as the number of inner peaks plus the number of inner valleys and called alternating runs in [2]