Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001895
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Mapping
St001895: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[-1] => 1
[1,2] => 0
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 2
[2,1] => 0
[2,-1] => 1
[-2,1] => 1
[-2,-1] => 0
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 2
[-1,2,3] => 1
[-1,2,-3] => 2
[-1,-2,3] => 2
[-1,-2,-3] => 3
[1,3,2] => 0
[1,3,-2] => 1
[1,-3,2] => 1
[1,-3,-2] => 0
[-1,3,2] => 1
[-1,3,-2] => 2
[-1,-3,2] => 2
[-1,-3,-2] => 1
[2,1,3] => 0
[2,1,-3] => 1
[2,-1,3] => 1
[2,-1,-3] => 2
[-2,1,3] => 1
[-2,1,-3] => 2
[-2,-1,3] => 0
[-2,-1,-3] => 1
[2,3,1] => 0
[2,3,-1] => 1
[2,-3,1] => 1
[2,-3,-1] => 0
[-2,3,1] => 1
[-2,3,-1] => 0
[-2,-3,1] => 0
[-2,-3,-1] => 1
[3,1,2] => 0
[3,1,-2] => 1
[3,-1,2] => 1
[3,-1,-2] => 0
[-3,1,2] => 1
[-3,1,-2] => 0
[-3,-1,2] => 0
[-3,-1,-2] => 1
Description
The oddness of a signed permutation. The direct sum of two signed permutations $\sigma\in\mathfrak H_k$ and $\tau\in\mathfrak H_m$ is the signed permutation in $\mathfrak H_{k+m}$ obtained by concatenating $\sigma$ with the result of increasing the absolute value of every entry in $\tau$ by $k$. This statistic records the number of blocks with an odd number of signs in the direct sum decomposition of a signed permutation.
Matching statistic: St001491
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 17% ●values known / values provided: 20%●distinct values known / distinct values provided: 17%
Values
[1] => []
 => []
 => => ? = 0 - 1
[-1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,2] => []
 => []
 => => ? = 0 - 1
[1,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-2] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[2,1] => []
 => []
 => => ? = 0 - 1
[2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[-2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[-2,-1] => []
 => []
 => => ? = 0 - 1
[1,2,3] => []
 => []
 => => ? = 0 - 1
[1,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[-1,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[-1,-2,3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[-1,-2,-3] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 3 - 1
[1,3,2] => []
 => []
 => => ? = 0 - 1
[1,3,-2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[1,-3,2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[1,-3,-2] => []
 => []
 => => ? = 0 - 1
[-1,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2 - 1
[-1,-3,2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2 - 1
[-1,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,1,3] => []
 => []
 => => ? = 0 - 1
[2,1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,-1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[2,-1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2 - 1
[-2,1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[-2,1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 2 - 1
[-2,-1,3] => []
 => []
 => => ? = 0 - 1
[-2,-1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,3,1] => []
 => []
 => => ? = 0 - 1
[2,3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[2,-3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[2,-3,-1] => []
 => []
 => => ? = 0 - 1
[-2,3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[-2,3,-1] => []
 => []
 => => ? = 0 - 1
[-2,-3,1] => []
 => []
 => => ? = 0 - 1
[-2,-3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[3,1,2] => []
 => []
 => => ? = 0 - 1
[3,1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[3,-1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[3,-1,-2] => []
 => []
 => => ? = 0 - 1
[-3,1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[-3,1,-2] => []
 => []
 => => ? = 0 - 1
[-3,-1,2] => []
 => []
 => => ? = 0 - 1
[-3,-1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1 - 1
[3,2,1] => []
 => []
 => => ? = 0 - 1
[3,2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[3,-2,1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[3,-2,-1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0 - 1
[-3,2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1 - 1
[-3,2,-1] => []
 => []
 => => ? = 0 - 1
[-3,-2,1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0 - 1
[-3,-2,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,2,3,4] => []
 => []
 => => ? = 0 - 1
[1,2,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,2,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,2,-3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[1,-2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[1,-2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 2 - 1
[-1,2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,3,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-3,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,3,2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-3,-2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,3,4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,3,-4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-3,4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-3,-4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,4,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,4,-2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-4,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-4,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,4,-3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[1,-4,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,4,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-1,-4,3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,-1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,-1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,-3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,-3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[2,-4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[-2,-4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[3,1,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
[3,-1,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0 = 1 - 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.