Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001241
(load all 5 compositions to match this statistic)
Mapping
St001241: 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]
 => 2
[1,0,1,0,1,0]
 => 0
[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]
 => 3
[1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => 0
[1,0,1,1,1,0,0,0]
 => 3
[1,1,0,0,1,0,1,0]
 => 1
[1,1,0,0,1,1,0,0]
 => 3
[1,1,0,1,0,0,1,0]
 => 0
[1,1,0,1,0,1,0,0]
 => 0
[1,1,0,1,1,0,0,0]
 => 2
[1,1,1,0,0,0,1,0]
 => 3
[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]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => 1
[1,0,1,0,1,1,0,1,0,0]
 => 0
[1,0,1,0,1,1,1,0,0,0]
 => 2
[1,0,1,1,0,0,1,0,1,0]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => 3
[1,0,1,1,0,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,1,0,0]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,0,1,0,0,0]
 => 0
[1,0,1,1,1,1,0,0,0,0]
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => 2
[1,1,0,0,1,1,0,0,1,0]
 => 3
[1,1,0,0,1,1,0,1,0,0]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => 4
[1,1,0,1,0,0,1,0,1,0]
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => 0
[1,1,0,1,0,1,0,1,0,0]
 => 0
[1,1,0,1,0,1,1,0,0,0]
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => 2
[1,1,0,1,1,0,0,1,0,0]
 => 0
[1,1,0,1,1,0,1,0,0,0]
 => 0
[1,1,0,1,1,1,0,0,0,0]
 => 3
Description
The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one.
Matching statistic: St000153
(load all 9 compositions to match this statistic)
Mapping
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000153: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => [1] => 1
[1,0,1,0]
 => [2,1] => [2,1] => 1
[1,1,0,0]
 => [1,2] => [1,2] => 2
[1,0,1,0,1,0]
 => [2,3,1] => [3,1,2] => 0
[1,0,1,1,0,0]
 => [2,1,3] => [2,1,3] => 2
[1,1,0,0,1,0]
 => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0]
 => [3,1,2] => [2,3,1] => 1
[1,1,1,0,0,0]
 => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0]
 => [2,3,4,1] => [4,1,2,3] => 0
[1,0,1,0,1,1,0,0]
 => [2,3,1,4] => [3,1,2,4] => 1
[1,0,1,1,0,0,1,0]
 => [2,1,4,3] => [2,1,4,3] => 2
[1,0,1,1,0,1,0,0]
 => [2,4,1,3] => [3,1,4,2] => 0
[1,0,1,1,1,0,0,0]
 => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,0,1,0]
 => [1,3,4,2] => [1,4,2,3] => 1
[1,1,0,0,1,1,0,0]
 => [1,3,2,4] => [1,3,2,4] => 3
[1,1,0,1,0,0,1,0]
 => [3,1,4,2] => [2,4,1,3] => 0
[1,1,0,1,0,1,0,0]
 => [3,4,1,2] => [3,4,1,2] => 0
[1,1,0,1,1,0,0,0]
 => [3,1,2,4] => [2,3,1,4] => 2
[1,1,1,0,0,0,1,0]
 => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [1,3,4,2] => 2
[1,1,1,0,1,0,0,0]
 => [4,1,2,3] => [2,3,4,1] => 1
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => [5,1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [2,3,4,1,5] => [4,1,2,3,5] => 1
[1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => [3,1,2,5,4] => 1
[1,0,1,0,1,1,0,1,0,0]
 => [2,3,5,1,4] => [4,1,2,5,3] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,3,1,4,5] => [3,1,2,4,5] => 2
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => [2,1,5,3,4] => 1
[1,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => 3
[1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => [3,1,5,2,4] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [2,4,5,1,3] => [4,1,5,2,3] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,4,1,3,5] => [3,1,4,2,5] => 1
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => [2,1,3,5,4] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [2,1,5,3,4] => [2,1,4,5,3] => 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => [3,1,4,5,2] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => [1,5,2,3,4] => 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,3,4,2,5] => [1,4,2,3,5] => 2
[1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,3,5,2,4] => [1,4,2,5,3] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => [2,5,1,3,4] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,1,4,2,5] => [2,4,1,3,5] => 1
[1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => [3,5,1,2,4] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,4,5,1,2] => [4,5,1,2,3] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,1,2,5] => [3,4,1,2,5] => 1
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,5,4] => [2,3,1,5,4] => 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => [2,4,1,5,3] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => [3,4,1,5,2] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [3,1,2,4,5] => [2,3,1,4,5] => 3
Description
The number of adjacent cycles of a permutation. This is the number of cycles of the permutation of the form (i,i+1,i+2,...i+k) which includes the fixed points (i).