Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001114
Mapping
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001114: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1] => [2] => [1,1,0,0]
 => [1,2] => 0
[1,1,1] => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 0
[1,2] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[2,1] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 0
[1,1,2] => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 1
[1,2,1] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[1,3] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[2,1,1] => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
[2,2] => [2] => [1,1,0,0]
 => [1,2] => 0
[3,1] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 0
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
[1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 1
[1,1,3] => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 1
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 1
[1,2,2] => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
[1,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[1,4] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 1
[2,1,2] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[2,2,1] => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 1
[2,3] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[3,1,1] => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 0
[3,2] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[4,1] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => 0
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 1
[1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 1
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 1
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
[1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 1
[1,1,4] => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 1
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => 1
[1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 2
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 2
[1,2,3] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 1
[1,3,2] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[1,4,1] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[1,5] => [1,1] => [1,0,1,0]
 => [2,1] => 1
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 0
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 2
[2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 2
[2,1,3] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 0
[2,2,2] => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 0
[2,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
[2,4] => [1,1] => [1,0,1,0]
 => [2,1] => 1
Description
The number of odd descents of a permutation.