Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001427
(load all 6 compositions to match this statistic)
Mapping
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
Mp00162: Signed permutations —inverse⟶ Signed permutations
St001427: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => 0
[-1] => [-1] => [-1] => 1
[1,2] => [1,2] => [1,2] => 0
[1,-2] => [1,-2] => [1,-2] => 1
[-1,2] => [-1,2] => [-1,2] => 1
[-1,-2] => [-1,-2] => [-1,-2] => 2
[2,1] => [-2,1] => [2,-1] => 1
[2,-1] => [-2,-1] => [-2,-1] => 1
[-2,1] => [2,1] => [2,1] => 1
[-2,-1] => [2,-1] => [-2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,-3] => [1,2,-3] => [1,2,-3] => 1
[1,-2,3] => [1,-2,3] => [1,-2,3] => 1
[1,-2,-3] => [1,-2,-3] => [1,-2,-3] => 2
[-1,2,3] => [-1,2,3] => [-1,2,3] => 1
[-1,2,-3] => [-1,2,-3] => [-1,2,-3] => 2
[-1,-2,3] => [-1,-2,3] => [-1,-2,3] => 2
[-1,-2,-3] => [-1,-2,-3] => [-1,-2,-3] => 3
[1,3,2] => [-3,1,2] => [2,3,-1] => 1
[1,3,-2] => [1,-3,-2] => [1,-3,-2] => 1
[1,-3,2] => [1,3,2] => [1,3,2] => 1
[1,-3,-2] => [3,1,-2] => [2,-3,1] => 1
[-1,3,2] => [-3,-1,2] => [-2,3,-1] => 2
[-1,3,-2] => [-1,-3,-2] => [-1,-3,-2] => 2
[-1,-3,2] => [-1,3,2] => [-1,3,2] => 2
[-1,-3,-2] => [3,-1,-2] => [-2,-3,1] => 2
[2,1,3] => [-2,1,3] => [2,-1,3] => 1
[2,1,-3] => [-2,1,-3] => [2,-1,-3] => 2
[2,-1,3] => [-2,-1,3] => [-2,-1,3] => 1
[2,-1,-3] => [-2,-1,-3] => [-2,-1,-3] => 2
[-2,1,3] => [2,1,3] => [2,1,3] => 1
[-2,1,-3] => [2,1,-3] => [2,1,-3] => 2
[-2,-1,3] => [2,-1,3] => [-2,1,3] => 1
[-2,-1,-3] => [2,-1,-3] => [-2,1,-3] => 2
[2,3,1] => [-3,-2,1] => [3,-2,-1] => 1
[2,3,-1] => [-3,-2,-1] => [-3,-2,-1] => 1
[2,-3,1] => [-3,2,1] => [3,2,-1] => 2
[2,-3,-1] => [-3,2,-1] => [-3,2,-1] => 2
[-2,3,1] => [3,-2,1] => [3,-2,1] => 1
[-2,3,-1] => [3,-2,-1] => [-3,-2,1] => 1
[-2,-3,1] => [3,2,1] => [3,2,1] => 2
[-2,-3,-1] => [3,2,-1] => [-3,2,1] => 2
[3,1,2] => [3,1,2] => [2,3,1] => 1
[3,1,-2] => [1,3,-2] => [1,-3,2] => 1
[3,-1,2] => [3,-1,2] => [-2,3,1] => 2
[3,-1,-2] => [-1,3,-2] => [-1,-3,2] => 2
[-3,1,2] => [1,-3,2] => [1,3,-2] => 1
[-3,1,-2] => [-3,1,-2] => [2,-3,-1] => 1
[-3,-1,2] => [-1,-3,2] => [-1,3,-2] => 2
[-3,-1,-2] => [-3,-1,-2] => [-2,-3,-1] => 2
Description
The number of descents of a signed permutation. A descent of a signed permutation $\sigma$ of length $n$ is an index $0 \leq i < n$ such that $\sigma(i) > \sigma(i+1)$, setting $\sigma(0) = 0$.
Matching statistic: St001896
(load all 12 compositions to match this statistic)
Mapping
Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00188: Signed permutations —complement⟶ Signed permutations
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
St001896: Signed permutations ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => [1] => 0
[-1] => [-1] => [-1] => [-1] => 1
[1,2] => [2,1] => [1,2] => [1,2] => 0
[1,-2] => [-2,1] => [-1,2] => [-1,2] => 1
[-1,2] => [2,-1] => [1,-2] => [1,-2] => 1
[-1,-2] => [-2,-1] => [-1,-2] => [-1,-2] => 2
[2,1] => [1,2] => [2,1] => [-2,1] => 1
[2,-1] => [-1,2] => [-2,1] => [2,1] => 1
[-2,1] => [1,-2] => [2,-1] => [-2,-1] => 1
[-2,-1] => [-1,-2] => [-2,-1] => [2,-1] => 1
[1,2,3] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,-3] => [-3,2,1] => [-1,2,3] => [-1,2,3] => 1
[1,-2,3] => [3,-2,1] => [1,-2,3] => [1,-2,3] => 1
[1,-2,-3] => [-3,-2,1] => [-1,-2,3] => [-1,-2,3] => 2
[-1,2,3] => [3,2,-1] => [1,2,-3] => [1,2,-3] => 1
[-1,2,-3] => [-3,2,-1] => [-1,2,-3] => [-1,2,-3] => 2
[-1,-2,3] => [3,-2,-1] => [1,-2,-3] => [1,-2,-3] => 2
[-1,-2,-3] => [-3,-2,-1] => [-1,-2,-3] => [-1,-2,-3] => 3
[1,3,2] => [2,3,1] => [2,1,3] => [-2,1,3] => 1
[1,3,-2] => [-2,3,1] => [-2,1,3] => [2,1,3] => 1
[1,-3,2] => [2,-3,1] => [2,-1,3] => [-2,-1,3] => 1
[1,-3,-2] => [-2,-3,1] => [-2,-1,3] => [2,-1,3] => 1
[-1,3,2] => [2,3,-1] => [2,1,-3] => [-2,1,-3] => 2
[-1,3,-2] => [-2,3,-1] => [-2,1,-3] => [2,1,-3] => 2
[-1,-3,2] => [2,-3,-1] => [2,-1,-3] => [-2,-1,-3] => 2
[-1,-3,-2] => [-2,-3,-1] => [-2,-1,-3] => [2,-1,-3] => 2
[2,1,3] => [3,1,2] => [1,3,2] => [-3,1,2] => 1
[2,1,-3] => [-3,1,2] => [-1,3,2] => [-3,-1,2] => 2
[2,-1,3] => [3,-1,2] => [1,-3,2] => [1,3,2] => 1
[2,-1,-3] => [-3,-1,2] => [-1,-3,2] => [-1,3,2] => 2
[-2,1,3] => [3,1,-2] => [1,3,-2] => [1,-3,-2] => 1
[-2,1,-3] => [-3,1,-2] => [-1,3,-2] => [-1,-3,-2] => 2
[-2,-1,3] => [3,-1,-2] => [1,-3,-2] => [3,1,-2] => 1
[-2,-1,-3] => [-3,-1,-2] => [-1,-3,-2] => [3,-1,-2] => 2
[2,3,1] => [1,3,2] => [3,1,2] => [3,1,2] => 1
[2,3,-1] => [-1,3,2] => [-3,1,2] => [1,-3,2] => 1
[2,-3,1] => [1,-3,2] => [3,-1,2] => [3,-1,2] => 2
[2,-3,-1] => [-1,-3,2] => [-3,-1,2] => [-1,-3,2] => 2
[-2,3,1] => [1,3,-2] => [3,1,-2] => [1,3,-2] => 1
[-2,3,-1] => [-1,3,-2] => [-3,1,-2] => [-3,1,-2] => 1
[-2,-3,1] => [1,-3,-2] => [3,-1,-2] => [-1,3,-2] => 2
[-2,-3,-1] => [-1,-3,-2] => [-3,-1,-2] => [-3,-1,-2] => 2
[3,1,2] => [2,1,3] => [2,3,1] => [-3,-2,1] => 1
[3,1,-2] => [-2,1,3] => [-2,3,1] => [3,-2,1] => 1
[3,-1,2] => [2,-1,3] => [2,-3,1] => [-3,2,1] => 2
[3,-1,-2] => [-2,-1,3] => [-2,-3,1] => [3,2,1] => 2
[-3,1,2] => [2,1,-3] => [2,3,-1] => [-3,-2,-1] => 1
[-3,1,-2] => [-2,1,-3] => [-2,3,-1] => [3,-2,-1] => 1
[-3,-1,2] => [2,-1,-3] => [2,-3,-1] => [-3,2,-1] => 2
[-3,-1,-2] => [-2,-1,-3] => [-2,-3,-1] => [3,2,-1] => 2
[1,2,3,5,4] => [4,5,3,2,1] => [2,1,3,4,5] => [-2,1,3,4,5] => ? = 1
[1,2,3,-5,4] => [4,-5,3,2,1] => [2,-1,3,4,5] => [-2,-1,3,4,5] => ? = 1
[1,2,3,-5,-4] => [-4,-5,3,2,1] => [-2,-1,3,4,5] => [2,-1,3,4,5] => ? = 1
[-1,2,3,-5,4] => [4,-5,3,2,-1] => [2,-1,3,4,-5] => [-2,-1,3,4,-5] => ? = 2
[-1,-2,-3,5,-4] => [-4,5,-3,-2,-1] => [-2,1,-3,-4,-5] => [2,1,-3,-4,-5] => ? = 4
[-1,-2,-3,-5,-4] => [-4,-5,-3,-2,-1] => [-2,-1,-3,-4,-5] => [2,-1,-3,-4,-5] => ? = 4
[1,2,4,3,5] => [5,3,4,2,1] => [1,3,2,4,5] => [-3,1,2,4,5] => ? = 1
[-1,-2,-4,-3,5] => [5,-3,-4,-2,-1] => [1,-3,-2,-4,-5] => [3,1,-2,-4,-5] => ? = 3
[1,2,4,-5,3] => [3,-5,4,2,1] => [3,-1,2,4,5] => [3,-1,2,4,5] => ? = 2
[1,2,-4,5,-3] => [-3,5,-4,2,1] => [-3,1,-2,4,5] => [-3,1,-2,4,5] => ? = 1
[1,2,-4,-5,-3] => [-3,-5,-4,2,1] => [-3,-1,-2,4,5] => [-3,-1,-2,4,5] => ? = 2
[1,-2,-4,5,-3] => [-3,5,-4,-2,1] => [-3,1,-2,-4,5] => [-3,1,-2,-4,5] => ? = 2
[1,2,5,3,4] => [4,3,5,2,1] => [2,3,1,4,5] => [-3,-2,1,4,5] => ? = 1
[1,2,5,3,-4] => [-4,3,5,2,1] => [-2,3,1,4,5] => [3,-2,1,4,5] => ? = 1
[1,2,-5,3,4] => [4,3,-5,2,1] => [2,3,-1,4,5] => [-3,-2,-1,4,5] => ? = 1
[-1,-2,-5,-3,-4] => [-4,-3,-5,-2,-1] => [-2,-3,-1,-4,-5] => [3,2,-1,-4,-5] => ? = 4
[1,2,5,4,3] => [3,4,5,2,1] => [3,2,1,4,5] => [2,-3,1,4,5] => ? = 2
[1,2,5,-4,3] => [3,-4,5,2,1] => [3,-2,1,4,5] => [2,3,1,4,5] => ? = 1
[1,2,5,-4,-3] => [-3,-4,5,2,1] => [-3,-2,1,4,5] => [-2,3,1,4,5] => ? = 1
[-1,2,5,-4,3] => [3,-4,5,2,-1] => [3,-2,1,4,-5] => [2,3,1,4,-5] => ? = 2
[-1,-2,-5,4,-3] => [-3,4,-5,-2,-1] => [-3,2,-1,-4,-5] => [-2,-3,-1,-4,-5] => ? = 4
[1,3,2,4,5] => [5,4,2,3,1] => [1,2,4,3,5] => [-4,1,2,3,5] => ? = 1
[1,3,2,-5,4] => [4,-5,2,3,1] => [2,-1,4,3,5] => [-4,-2,-1,3,5] => ? = 2
[1,-3,2,-5,4] => [4,-5,2,-3,1] => [2,-1,4,-3,5] => [-2,-1,-4,-3,5] => ? = 2
[1,-3,2,-5,-4] => [-4,-5,2,-3,1] => [-2,-1,4,-3,5] => [2,-1,-4,-3,5] => ? = 2
[1,-3,-2,-5,-4] => [-4,-5,-2,-3,1] => [-2,-1,-4,-3,5] => [4,2,-1,-3,5] => ? = 2
[-1,3,-2,5,-4] => [-4,5,-2,3,-1] => [-2,1,-4,3,-5] => [2,1,4,3,-5] => ? = 3
[-1,-3,2,-5,4] => [4,-5,2,-3,-1] => [2,-1,4,-3,-5] => [-2,-1,-4,-3,-5] => ? = 3
[1,3,-4,-5,2] => [2,-5,-4,3,1] => [4,-1,-2,3,5] => [-4,-1,-2,3,5] => ? = 3
[1,-3,4,5,-2] => [-2,5,4,-3,1] => [-4,1,2,-3,5] => [4,1,2,-3,5] => ? = 1
[1,-3,4,-5,2] => [2,-5,4,-3,1] => [4,-1,2,-3,5] => [-4,-1,2,-3,5] => ? = 2
[1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => [2,-4,1,3,5] => ? = 2
[1,-3,5,2,4] => [4,2,5,-3,1] => [2,4,1,-3,5] => [-2,1,4,-3,5] => ? = 2
[1,-3,5,2,-4] => [-4,2,5,-3,1] => [-2,4,1,-3,5] => [2,1,4,-3,5] => ? = 2
[1,-3,-5,2,4] => [4,2,-5,-3,1] => [2,4,-1,-3,5] => [-2,-1,4,-3,5] => ? = 2
[-1,3,-5,-2,-4] => [-4,-2,-5,3,-1] => [-2,-4,-1,3,-5] => [2,-1,-4,3,-5] => ? = 3
[-1,-3,5,2,4] => [4,2,5,-3,-1] => [2,4,1,-3,-5] => [-2,1,4,-3,-5] => ? = 3
[-1,-3,5,-2,-4] => [-4,-2,5,-3,-1] => [-2,-4,1,-3,-5] => [-2,4,1,-3,-5] => ? = 3
[1,3,5,-4,2] => [2,-4,5,3,1] => [4,-2,1,3,5] => [-2,4,1,3,5] => ? = 2
[1,3,-5,-4,2] => [2,-4,-5,3,1] => [4,-2,-1,3,5] => [-2,4,-1,3,5] => ? = 2
[1,3,-5,-4,-2] => [-2,-4,-5,3,1] => [-4,-2,-1,3,5] => [4,2,-1,3,5] => ? = 2
[1,-3,5,-4,2] => [2,-4,5,-3,1] => [4,-2,1,-3,5] => [4,-2,1,-3,5] => ? = 2
[1,-3,5,-4,-2] => [-2,-4,5,-3,1] => [-4,-2,1,-3,5] => [2,4,1,-3,5] => ? = 2
[-1,3,-5,4,-2] => [-2,4,-5,3,-1] => [-4,2,-1,3,-5] => [-4,2,-1,3,-5] => ? = 3
[-1,3,-5,-4,2] => [2,-4,-5,3,-1] => [4,-2,-1,3,-5] => [-2,4,-1,3,-5] => ? = 3
[-1,3,-5,-4,-2] => [-2,-4,-5,3,-1] => [-4,-2,-1,3,-5] => [4,2,-1,3,-5] => ? = 3
[-1,-3,5,4,-2] => [-2,4,5,-3,-1] => [-4,2,1,-3,-5] => [2,-4,1,-3,-5] => ? = 3
[-1,-3,5,-4,2] => [2,-4,5,-3,-1] => [4,-2,1,-3,-5] => [4,-2,1,-3,-5] => ? = 3
[1,4,2,3,5] => [5,3,2,4,1] => [1,3,4,2,5] => [-4,-3,1,2,5] => ? = 1
[1,4,2,3,-5] => [-5,3,2,4,1] => [-1,3,4,2,5] => [-4,-3,-1,2,5] => ? = 2
Description
The number of right descents of a signed permutations. An index is a right descent if it is a left descent of the inverse signed permutation.