Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001086
Mapping
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St001086: 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]
 => [2,1,3] => [3,2,1] => [3,2,1] => 0
[1,0,1,1,0,0]
 => [2,3,1] => [3,1,2] => [1,3,2] => 1
[1,1,0,0,1,0]
 => [3,1,2] => [1,3,2] => [2,3,1] => 0
[1,1,0,1,0,0]
 => [1,3,2] => [2,1,3] => [2,1,3] => 0
[1,1,1,0,0,0]
 => [1,2,3] => [2,3,1] => [3,1,2] => 0
[1,0,1,0,1,0,1,0]
 => [2,1,4,3] => [3,2,1,4] => [3,2,1,4] => 0
[1,0,1,0,1,1,0,0]
 => [2,4,1,3] => [3,1,4,2] => [3,4,1,2] => 0
[1,0,1,1,0,0,1,0]
 => [2,1,3,4] => [3,2,4,1] => [4,2,1,3] => 0
[1,0,1,1,0,1,0,0]
 => [2,3,1,4] => [3,4,2,1] => [4,3,1,2] => 0
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [3,4,1,2] => [1,4,2,3] => 1
[1,1,0,0,1,0,1,0]
 => [3,1,4,2] => [4,2,1,3] => [3,1,4,2] => 1
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [4,1,3,2] => [2,4,3,1] => 1
[1,1,0,1,0,0,1,0]
 => [3,1,2,4] => [4,2,3,1] => [4,1,3,2] => 1
[1,1,0,1,0,1,0,0]
 => [1,3,2,4] => [2,4,3,1] => [4,2,3,1] => 0
[1,1,0,1,1,0,0,0]
 => [1,3,4,2] => [2,4,1,3] => [1,3,4,2] => 0
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [1,3,4,2] => [2,4,1,3] => 0
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [2,1,4,3] => [3,2,4,1] => 0
[1,1,1,0,1,0,0,0]
 => [1,2,4,3] => [2,3,1,4] => [3,1,2,4] => 0
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [2,3,4,1] => [4,1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [2,1,4,3,5] => [3,2,5,4,1] => [5,3,2,4,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => [3,5,2,4,1] => [5,1,3,4,2] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [2,1,4,5,3] => [3,2,5,1,4] => [1,4,3,5,2] => 1
[1,0,1,0,1,1,0,1,0,0]
 => [2,4,1,5,3] => [3,5,2,1,4] => [4,1,3,5,2] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,4,5,1,3] => [3,5,1,4,2] => [2,5,3,4,1] => 1
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,5,3,4] => [3,2,1,5,4] => [4,3,2,5,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [2,5,1,3,4] => [3,1,4,5,2] => [3,5,1,2,4] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [2,1,3,5,4] => [3,2,4,1,5] => [4,2,1,3,5] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => [3,4,2,1,5] => [4,3,1,2,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,3,5,1,4] => [3,4,1,5,2] => [4,5,1,2,3] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,4,5] => [3,2,4,5,1] => [5,2,1,3,4] => 0
[1,0,1,1,1,0,0,1,0,0]
 => [2,3,1,4,5] => [3,4,2,5,1] => [5,3,1,2,4] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,3,4,1,5] => [3,4,5,2,1] => [5,4,1,2,3] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [3,4,5,1,2] => [1,5,2,3,4] => 1
[1,1,0,0,1,0,1,0,1,0]
 => [3,1,4,2,5] => [4,2,5,3,1] => [5,3,4,1,2] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,4,1,2,5] => [4,5,2,3,1] => [5,1,4,2,3] => 1
[1,1,0,0,1,1,0,0,1,0]
 => [3,1,4,5,2] => [4,2,5,1,3] => [1,4,5,2,3] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [3,4,1,5,2] => [4,5,2,1,3] => [4,1,5,2,3] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [4,5,1,3,2] => [2,5,4,1,3] => 1
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,5,2,4] => [4,2,1,5,3] => [4,3,5,1,2] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,5,1,2,4] => [4,1,3,5,2] => [2,5,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,0]
 => [3,1,2,5,4] => [4,2,3,1,5] => [4,1,3,2,5] => 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => [2,4,3,1,5] => [4,2,3,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => [2,4,1,5,3] => [4,2,5,1,3] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,4,5] => [4,2,3,5,1] => [5,1,3,2,4] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,3,2,4,5] => [2,4,3,5,1] => [5,2,3,1,4] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [1,3,4,2,5] => [2,4,5,3,1] => [5,2,4,1,3] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [1,3,4,5,2] => [2,4,5,1,3] => [1,3,5,2,4] => 0
Description
The number of occurrences of the consecutive pattern 132 in a permutation. This is the number of occurrences of the pattern $132$, where the matched entries are all adjacent.