Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000489
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Mapping
St000489: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 2
[2,1] => 1
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 0
[3,2,1,4] => 3
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 3
[4,3,1,2] => 0
[4,3,2,1] => 2
[1,2,3,4,5] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 3
[1,2,5,3,4] => 3
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 1
[1,3,5,2,4] => 1
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 1
[1,4,3,2,5] => 4
[1,4,3,5,2] => 3
[1,4,5,2,3] => 3
[1,4,5,3,2] => 1
Description
The number of cycles of a permutation of length at most 3.
Matching statistic: St001200
Mapping
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 38%
Values
[1,2] => [1,2] => [1,0,1,0]
 => [1,1,0,1,0,0]
 => 2
[2,1] => [2,1] => [1,1,0,0]
 => [1,1,1,0,0,0]
 => ? = 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 3
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[2,3,1] => [3,1,2] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 1
[3,1,2] => [3,2,1] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ? = 1
[3,2,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => 2
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 3
[1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 2
[1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 2
[1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => 3
[2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 3
[2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 2
[2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[2,4,3,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
[3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3
[3,2,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
[3,4,1,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 2
[3,4,2,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
[4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
[4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
[4,3,1,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? = 0
[4,3,2,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 5
[1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 4
[1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => ? = 4
[1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => ? = 3
[1,2,5,3,4] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => ? = 3
[1,2,5,4,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => ? = 4
[1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 4
[1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => ? = 3
[1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => ? = 3
[1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,3,5,2,4] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,3,5,4,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => ? = 3
[1,4,2,3,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => ? = 3
[1,4,2,5,3] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,4,3,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => ? = 4
[1,4,3,5,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => ? = 3
[1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => ? = 3
[1,4,5,3,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,5,2,3,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,5,2,4,3] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => ? = 3
[1,5,3,2,4] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => ? = 3
[1,5,3,4,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 4
[1,5,4,2,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 1
[1,5,4,3,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => ? = 3
[2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => ? = 4
[2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ? = 3
[2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => ? = 3
[2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ? = 2
[2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ? = 2
[2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => ? = 3
[2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => ? = 3
[2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => ? = 2
[2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => ? = 1
[2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 0
[2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 0
[2,3,5,4,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => ? = 1
[2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => ? = 1
[2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 0
[2,4,3,1,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => ? = 3
[2,4,3,5,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => ? = 1
[2,4,5,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => ? = 2
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.