Your data matches 2 different statistics following compositions of up to 3 maps.
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St001872: 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]
=> 3
[1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> 3
[1,0,1,1,0,0]
=> 3
[1,1,0,0,1,0]
=> 3
[1,1,0,1,0,0]
=> 4
[1,1,1,0,0,0]
=> 1
[1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,1,0,0]
=> 3
[1,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,0,0]
=> 3
[1,0,1,1,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,0]
=> 3
[1,1,0,0,1,1,0,0]
=> 3
[1,1,0,1,0,0,1,0]
=> 4
[1,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,1,0,0,0]
=> 4
[1,1,1,0,0,0,1,0]
=> 3
[1,1,1,0,0,1,0,0]
=> 4
[1,1,1,0,1,0,0,0]
=> 5
[1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,0,1,1,0,0]
=> 5
[1,0,1,0,1,1,0,0,1,0]
=> 5
[1,0,1,0,1,1,0,1,0,0]
=> 6
[1,0,1,0,1,1,1,0,0,0]
=> 3
[1,0,1,1,0,0,1,0,1,0]
=> 5
[1,0,1,1,0,0,1,1,0,0]
=> 5
[1,0,1,1,0,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,0,1,0,0]
=> 6
[1,0,1,1,0,1,1,0,0,0]
=> 3
[1,0,1,1,1,0,0,0,1,0]
=> 5
[1,0,1,1,1,0,0,1,0,0]
=> 6
[1,0,1,1,1,0,1,0,0,0]
=> 3
[1,0,1,1,1,1,0,0,0,0]
=> 3
[1,1,0,0,1,0,1,0,1,0]
=> 5
[1,1,0,0,1,0,1,1,0,0]
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,0,1,1,0,1,0,0]
=> 3
[1,1,0,0,1,1,1,0,0,0]
=> 3
[1,1,0,1,0,0,1,0,1,0]
=> 6
[1,1,0,1,0,0,1,1,0,0]
=> 4
[1,1,0,1,0,1,0,0,1,0]
=> 6
[1,1,0,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,0,1,1,0,0,0]
=> 4
[1,1,0,1,1,0,0,0,1,0]
=> 6
[1,1,0,1,1,0,0,1,0,0]
=> 4
[1,1,0,1,1,0,1,0,0,0]
=> 4
[1,1,0,1,1,1,0,0,0,0]
=> 4
Description
The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra.
Mp00028: Dyck paths reverseDyck paths
St001473: Dyck paths ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1,0]
=> 1
[1,0,1,0]
=> [1,0,1,0]
=> 3
[1,1,0,0]
=> [1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> 3
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 3
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> 3
[1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> 4
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> 1
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> 3
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 3
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> 3
[1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 3
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> 4
[1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 4
[1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 5
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 5
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> 6
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 3
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> 6
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> 3
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 5
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 6
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 3
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 5
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 5
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 3
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> 6
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 4
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> 6
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 4
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 6
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 4
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 4
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 4
Description
The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra.