Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000955
(load all 2 compositions to match this statistic)
Mapping
St000955: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 1
[1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => 2
[1,1,0,1,0,0]
 => 1
[1,1,1,0,0,0]
 => 1
[1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => 2
[1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => 2
[1,0,1,1,1,0,0,0]
 => 2
[1,1,0,0,1,0,1,0]
 => 2
[1,1,0,0,1,1,0,0]
 => 2
[1,1,0,1,0,0,1,0]
 => 2
[1,1,0,1,0,1,0,0]
 => 2
[1,1,0,1,1,0,0,0]
 => 2
[1,1,1,0,0,0,1,0]
 => 2
[1,1,1,0,0,1,0,0]
 => 2
[1,1,1,0,1,0,0,0]
 => 1
[1,1,1,1,0,0,0,0]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => 3
[1,0,1,0,1,1,0,1,0,0]
 => 2
[1,0,1,0,1,1,1,0,0,0]
 => 2
[1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,0,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,1,0,0]
 => 2
[1,0,1,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,0,0,0,1,0]
 => 2
[1,0,1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,0,1,0,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => 2
[1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,0,0,1,1,0,1,0,0]
 => 3
[1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => 2
[1,1,0,1,0,0,1,1,0,0]
 => 3
[1,1,0,1,0,1,0,0,1,0]
 => 2
[1,1,0,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,0,0,0,1,0]
 => 2
[1,1,0,1,1,0,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,0,0,0]
 => 2
[1,1,0,1,1,1,0,0,0,0]
 => 2
Description
Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra.
Matching statistic: St001569
(load all 3 compositions to match this statistic)
Mapping
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
St001569: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
[1,0]
 => [1,0]
 => [2,1] => [2,1] => 1
[1,0,1,0]
 => [1,0,1,0]
 => [3,1,2] => [2,3,1] => 1
[1,1,0,0]
 => [1,1,0,0]
 => [2,3,1] => [3,1,2] => 1
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => [2,3,4,1] => 1
[1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => [2,4,3,1] => 2
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => [3,4,1,2] => 2
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => [4,2,3,1] => 1
[1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => [4,1,2,3] => 1
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => [2,3,4,5,1] => 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => [2,3,5,4,1] => 2
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => [2,4,5,3,1] => 2
[1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => [3,4,2,5,1] => 2
[1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [5,3,4,1,2] => [2,4,1,5,3] => 2
[1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => [3,4,5,1,2] => 2
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => [3,5,4,1,2] => 2
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => [4,5,2,3,1] => 2
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => [2,5,3,4,1] => 2
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => [5,2,3,1,4] => 2
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => [4,5,1,2,3] => 2
[1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => [5,3,4,1,2] => 2
[1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,0,0]
 => [4,3,1,5,2] => [5,2,4,3,1] => 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [5,1,2,3,4] => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [6,1,2,3,4,5] => [2,3,4,5,6,1] => ? = 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => [2,3,4,6,1,5] => ? = 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => [2,3,5,6,4,1] => ? = 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => [3,4,5,2,6,1] => ? = 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [6,5,4,1,2,3] => [2,3,6,5,4,1] => ? = 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [6,3,1,2,4,5] => [2,4,5,6,3,1] => ? = 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [6,3,5,1,2,4] => [2,4,5,1,6,3] => ? = 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [6,1,4,2,3,5] => [3,4,2,5,6,1] => ? = 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => [2,4,5,3,6,1] => ? = 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => [3,5,2,4,6,1] => ? = 3
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => [2,4,1,5,6,3] => ? = 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [6,3,1,5,2,4] => [4,5,2,6,3,1] => ? = 2
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [6,4,1,5,2,3] => [3,5,2,6,4,1] => ? = 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [6,3,4,5,1,2] => [2,5,1,4,6,3] => ? = 2
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,6,1,3,4,5] => [3,4,5,6,1,2] => ? = 2
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => [3,4,6,5,1,2] => ? = 2
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => [3,5,6,4,1,2] => ? = 2
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => [4,5,3,6,1,2] => ? = 3
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [2,6,4,5,1,3] => [3,5,1,2,6,4] => ? = 2
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [3,1,6,2,4,5] => [4,5,6,2,3,1] => ? = 2
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => [4,6,5,2,3,1] => ? = 3
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [4,1,2,6,3,5] => [2,5,6,3,4,1] => ? = 2
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => [2,3,6,4,5,1] => ? = 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => [2,6,3,4,1,5] => ? = 3
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => [5,6,2,3,1,4] => ? = 2
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => [6,4,5,2,3,1] => ? = 3
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => [6,3,4,2,5,1] => ? = 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => [6,2,3,1,4,5] => ? = 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => [4,5,6,1,2,3] => ? = 2
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => [4,6,5,1,2,3] => ? = 2
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => [5,6,3,4,1,2] => ? = 3
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,5,1,3,6,4] => [3,6,4,5,1,2] => ? = 3
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => [6,3,4,1,2,5] => ? = 2
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => [5,6,2,4,3,1] => ? = 2
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => [2,6,4,5,3,1] => ? = 2
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [5,4,1,2,6,3] => [2,6,3,5,4,1] => ? = 2
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [4,3,1,5,6,2] => [6,2,4,3,1,5] => ? = 2
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => [5,6,1,2,3,4] => ? = 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => [6,4,5,1,2,3] => ? = 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [2,5,4,1,6,3] => [6,3,5,4,1,2] => ? = 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,3,4,1,6,2] => [6,2,4,1,5,3] => ? = 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => [6,1,2,3,4,5] => ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [7,6,1,2,3,4,5] => [2,3,4,5,7,6,1] => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [5,7,1,2,3,4,6] => [2,3,4,6,7,1,5] => ? = 3
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [6,1,7,2,3,4,5] => [3,4,5,7,2,6,1] => ? = 2
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,7,5,1,2,3,4] => [2,3,4,7,5,1,6] => ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [7,4,1,2,3,5,6] => [2,3,5,6,7,4,1] => ? = 2
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [6,7,4,1,2,3,5] => [2,3,5,7,4,1,6] => ? = 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [7,1,5,2,3,4,6] => [3,4,5,2,6,7,1] => ? = 3
Description
The maximal modular displacement of a permutation. This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.