Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001405
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Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St001405: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => 0
[1,0,1,0]
 => [1,2] => 1
[1,1,0,0]
 => [2,1] => 1
[1,0,1,0,1,0]
 => [1,2,3] => 2
[1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1,0,0,1,0]
 => [2,1,3] => 1
[1,1,0,1,0,0]
 => [2,3,1] => 1
[1,1,1,0,0,0]
 => [3,2,1] => 2
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 3
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 2
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 2
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 2
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => 1
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => 2
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 1
[1,1,1,0,1,0,0,0]
 => [3,4,2,1] => 2
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => 4
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => 2
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => 3
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => 3
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => 2
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => 3
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => 2
Description
The number of bonds in a permutation. For a permutation $\pi$, the pair $(\pi_i, \pi_{i+1})$ is a bond if $|\pi_i-\pi_{i+1}| = 1$.