Processing math: 100%

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001817
(load all 4 compositions to match this statistic)
Mapping
St001817: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 2
[-1] => 1
[1,2] => 4
[1,-2] => 3
[-1,2] => 3
[-1,-2] => 2
[2,1] => 2
[2,-1] => 3
[-2,1] => 1
[-2,-1] => 2
[1,2,3] => 6
[1,2,-3] => 5
[1,-2,3] => 5
[1,-2,-3] => 4
[-1,2,3] => 5
[-1,2,-3] => 4
[-1,-2,3] => 4
[-1,-2,-3] => 3
[1,3,2] => 4
[1,3,-2] => 5
[1,-3,2] => 3
[1,-3,-2] => 4
[-1,3,2] => 3
[-1,3,-2] => 4
[-1,-3,2] => 2
[-1,-3,-2] => 3
[2,1,3] => 4
[2,1,-3] => 3
[2,-1,3] => 5
[2,-1,-3] => 4
[-2,1,3] => 3
[-2,1,-3] => 2
[-2,-1,3] => 4
[-2,-1,-3] => 3
[2,3,1] => 4
[2,3,-1] => 5
[2,-3,1] => 3
[2,-3,-1] => 4
[-2,3,1] => 3
[-2,3,-1] => 4
[-2,-3,1] => 2
[-2,-3,-1] => 3
[3,1,2] => 2
[3,1,-2] => 3
[3,-1,2] => 3
[3,-1,-2] => 4
[-3,1,2] => 1
[-3,1,-2] => 2
[-3,-1,2] => 2
[-3,-1,-2] => 3
Description
The number of flag weak exceedances of a signed permutation. This is the number of negative entries plus twice the number of weak exceedances of the signed permutation.
Matching statistic: St001892
(load all 4 compositions to match this statistic)
Mapping
Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00188: Signed permutations —complement⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
St001892: Signed permutations ⟶ ℤResult quality: 53% ●values known / values provided: 53%●distinct values known / distinct values provided: 90%
Values
[1] => [1] => [1] => [-1] => 1 = 2 - 1
[-1] => [-1] => [-1] => [1] => 0 = 1 - 1
[1,2] => [2,1] => [1,2] => [2,-1] => 3 = 4 - 1
[1,-2] => [-2,1] => [-1,2] => [2,1] => 2 = 3 - 1
[-1,2] => [2,-1] => [1,-2] => [-2,-1] => 2 = 3 - 1
[-1,-2] => [-2,-1] => [-1,-2] => [-2,1] => 1 = 2 - 1
[2,1] => [1,2] => [2,1] => [1,-2] => 1 = 2 - 1
[2,-1] => [-1,2] => [-2,1] => [-1,-2] => 2 = 3 - 1
[-2,1] => [1,-2] => [2,-1] => [1,2] => 0 = 1 - 1
[-2,-1] => [-1,-2] => [-2,-1] => [-1,2] => 1 = 2 - 1
[1,2,3] => [3,2,1] => [1,2,3] => [2,3,-1] => 5 = 6 - 1
[1,2,-3] => [-3,2,1] => [-1,2,3] => [2,3,1] => 4 = 5 - 1
[1,-2,3] => [3,-2,1] => [1,-2,3] => [-2,3,-1] => 4 = 5 - 1
[1,-2,-3] => [-3,-2,1] => [-1,-2,3] => [-2,3,1] => 3 = 4 - 1
[-1,2,3] => [3,2,-1] => [1,2,-3] => [2,-3,-1] => 4 = 5 - 1
[-1,2,-3] => [-3,2,-1] => [-1,2,-3] => [2,-3,1] => 3 = 4 - 1
[-1,-2,3] => [3,-2,-1] => [1,-2,-3] => [-2,-3,-1] => 3 = 4 - 1
[-1,-2,-3] => [-3,-2,-1] => [-1,-2,-3] => [-2,-3,1] => 2 = 3 - 1
[1,3,2] => [2,3,1] => [2,1,3] => [1,3,-2] => 3 = 4 - 1
[1,3,-2] => [-2,3,1] => [-2,1,3] => [-1,3,-2] => 4 = 5 - 1
[1,-3,2] => [2,-3,1] => [2,-1,3] => [1,3,2] => 2 = 3 - 1
[1,-3,-2] => [-2,-3,1] => [-2,-1,3] => [-1,3,2] => 3 = 4 - 1
[-1,3,2] => [2,3,-1] => [2,1,-3] => [1,-3,-2] => 2 = 3 - 1
[-1,3,-2] => [-2,3,-1] => [-2,1,-3] => [-1,-3,-2] => 3 = 4 - 1
[-1,-3,2] => [2,-3,-1] => [2,-1,-3] => [1,-3,2] => 1 = 2 - 1
[-1,-3,-2] => [-2,-3,-1] => [-2,-1,-3] => [-1,-3,2] => 2 = 3 - 1
[2,1,3] => [3,1,2] => [1,3,2] => [3,2,-1] => 3 = 4 - 1
[2,1,-3] => [-3,1,2] => [-1,3,2] => [3,2,1] => 2 = 3 - 1
[2,-1,3] => [3,-1,2] => [1,-3,2] => [3,-2,-1] => 4 = 5 - 1
[2,-1,-3] => [-3,-1,2] => [-1,-3,2] => [3,-2,1] => 3 = 4 - 1
[-2,1,3] => [3,1,-2] => [1,3,-2] => [-3,2,-1] => 2 = 3 - 1
[-2,1,-3] => [-3,1,-2] => [-1,3,-2] => [-3,2,1] => 1 = 2 - 1
[-2,-1,3] => [3,-1,-2] => [1,-3,-2] => [-3,-2,-1] => 3 = 4 - 1
[-2,-1,-3] => [-3,-1,-2] => [-1,-3,-2] => [-3,-2,1] => 2 = 3 - 1
[2,3,1] => [1,3,2] => [3,1,2] => [3,1,-2] => 3 = 4 - 1
[2,3,-1] => [-1,3,2] => [-3,1,2] => [3,-1,-2] => 4 = 5 - 1
[2,-3,1] => [1,-3,2] => [3,-1,2] => [3,1,2] => 2 = 3 - 1
[2,-3,-1] => [-1,-3,2] => [-3,-1,2] => [3,-1,2] => 3 = 4 - 1
[-2,3,1] => [1,3,-2] => [3,1,-2] => [-3,1,-2] => 2 = 3 - 1
[-2,3,-1] => [-1,3,-2] => [-3,1,-2] => [-3,-1,-2] => 3 = 4 - 1
[-2,-3,1] => [1,-3,-2] => [3,-1,-2] => [-3,1,2] => 1 = 2 - 1
[-2,-3,-1] => [-1,-3,-2] => [-3,-1,-2] => [-3,-1,2] => 2 = 3 - 1
[3,1,2] => [2,1,3] => [2,3,1] => [1,2,-3] => 1 = 2 - 1
[3,1,-2] => [-2,1,3] => [-2,3,1] => [-1,2,-3] => 2 = 3 - 1
[3,-1,2] => [2,-1,3] => [2,-3,1] => [1,-2,-3] => 2 = 3 - 1
[3,-1,-2] => [-2,-1,3] => [-2,-3,1] => [-1,-2,-3] => 3 = 4 - 1
[-3,1,2] => [2,1,-3] => [2,3,-1] => [1,2,3] => 0 = 1 - 1
[-3,1,-2] => [-2,1,-3] => [-2,3,-1] => [-1,2,3] => 1 = 2 - 1
[-3,-1,2] => [2,-1,-3] => [2,-3,-1] => [1,-2,3] => 1 = 2 - 1
[-3,-1,-2] => [-2,-1,-3] => [-2,-3,-1] => [-1,-2,3] => 2 = 3 - 1
[1,2,3,4,5] => [5,4,3,2,1] => [1,2,3,4,5] => [2,3,4,5,-1] => ? = 10 - 1
[1,2,3,4,-5] => [-5,4,3,2,1] => [-1,2,3,4,5] => [2,3,4,5,1] => ? = 9 - 1
[1,2,3,-4,5] => [5,-4,3,2,1] => [1,-2,3,4,5] => [-2,3,4,5,-1] => ? = 9 - 1
[1,2,3,-4,-5] => [-5,-4,3,2,1] => [-1,-2,3,4,5] => [-2,3,4,5,1] => ? = 8 - 1
[1,2,-3,4,5] => [5,4,-3,2,1] => [1,2,-3,4,5] => [2,-3,4,5,-1] => ? = 9 - 1
[1,2,-3,4,-5] => [-5,4,-3,2,1] => [-1,2,-3,4,5] => [2,-3,4,5,1] => ? = 8 - 1
[1,2,-3,-4,5] => [5,-4,-3,2,1] => [1,-2,-3,4,5] => [-2,-3,4,5,-1] => ? = 8 - 1
[1,2,-3,-4,-5] => [-5,-4,-3,2,1] => [-1,-2,-3,4,5] => [-2,-3,4,5,1] => ? = 7 - 1
[1,-2,3,4,5] => [5,4,3,-2,1] => [1,2,3,-4,5] => [2,3,-4,5,-1] => ? = 9 - 1
[1,-2,3,4,-5] => [-5,4,3,-2,1] => [-1,2,3,-4,5] => [2,3,-4,5,1] => ? = 8 - 1
[1,-2,3,-4,5] => [5,-4,3,-2,1] => [1,-2,3,-4,5] => [-2,3,-4,5,-1] => ? = 8 - 1
[1,-2,3,-4,-5] => [-5,-4,3,-2,1] => [-1,-2,3,-4,5] => [-2,3,-4,5,1] => ? = 7 - 1
[1,-2,-3,4,5] => [5,4,-3,-2,1] => [1,2,-3,-4,5] => [2,-3,-4,5,-1] => ? = 8 - 1
[1,-2,-3,4,-5] => [-5,4,-3,-2,1] => [-1,2,-3,-4,5] => [2,-3,-4,5,1] => ? = 7 - 1
[1,-2,-3,-4,5] => [5,-4,-3,-2,1] => [1,-2,-3,-4,5] => [-2,-3,-4,5,-1] => ? = 7 - 1
[1,-2,-3,-4,-5] => [-5,-4,-3,-2,1] => [-1,-2,-3,-4,5] => [-2,-3,-4,5,1] => ? = 6 - 1
[-1,2,3,4,5] => [5,4,3,2,-1] => [1,2,3,4,-5] => [2,3,4,-5,-1] => ? = 9 - 1
[-1,2,3,4,-5] => [-5,4,3,2,-1] => [-1,2,3,4,-5] => [2,3,4,-5,1] => ? = 8 - 1
[-1,2,3,-4,5] => [5,-4,3,2,-1] => [1,-2,3,4,-5] => [-2,3,4,-5,-1] => ? = 8 - 1
[-1,2,3,-4,-5] => [-5,-4,3,2,-1] => [-1,-2,3,4,-5] => [-2,3,4,-5,1] => ? = 7 - 1
[-1,2,-3,4,5] => [5,4,-3,2,-1] => [1,2,-3,4,-5] => [2,-3,4,-5,-1] => ? = 8 - 1
[-1,2,-3,4,-5] => [-5,4,-3,2,-1] => [-1,2,-3,4,-5] => [2,-3,4,-5,1] => ? = 7 - 1
[-1,2,-3,-4,5] => [5,-4,-3,2,-1] => [1,-2,-3,4,-5] => [-2,-3,4,-5,-1] => ? = 7 - 1
[-1,2,-3,-4,-5] => [-5,-4,-3,2,-1] => [-1,-2,-3,4,-5] => [-2,-3,4,-5,1] => ? = 6 - 1
[-1,-2,3,4,5] => [5,4,3,-2,-1] => [1,2,3,-4,-5] => [2,3,-4,-5,-1] => ? = 8 - 1
[-1,-2,3,4,-5] => [-5,4,3,-2,-1] => [-1,2,3,-4,-5] => [2,3,-4,-5,1] => ? = 7 - 1
[-1,-2,3,-4,5] => [5,-4,3,-2,-1] => [1,-2,3,-4,-5] => [-2,3,-4,-5,-1] => ? = 7 - 1
[-1,-2,3,-4,-5] => [-5,-4,3,-2,-1] => [-1,-2,3,-4,-5] => [-2,3,-4,-5,1] => ? = 6 - 1
[-1,-2,-3,4,5] => [5,4,-3,-2,-1] => [1,2,-3,-4,-5] => [2,-3,-4,-5,-1] => ? = 7 - 1
[-1,-2,-3,4,-5] => [-5,4,-3,-2,-1] => [-1,2,-3,-4,-5] => [2,-3,-4,-5,1] => ? = 6 - 1
[-1,-2,-3,-4,5] => [5,-4,-3,-2,-1] => [1,-2,-3,-4,-5] => [-2,-3,-4,-5,-1] => ? = 6 - 1
[-1,-2,-3,-4,-5] => [-5,-4,-3,-2,-1] => [-1,-2,-3,-4,-5] => [-2,-3,-4,-5,1] => ? = 5 - 1
[1,2,4,3,5] => [5,3,4,2,1] => [1,3,2,4,5] => [3,2,4,5,-1] => ? = 8 - 1
[1,2,4,3,-5] => [-5,3,4,2,1] => [-1,3,2,4,5] => [3,2,4,5,1] => ? = 7 - 1
[1,2,4,-3,5] => [5,-3,4,2,1] => [1,-3,2,4,5] => [3,-2,4,5,-1] => ? = 9 - 1
[1,2,4,-3,-5] => [-5,-3,4,2,1] => [-1,-3,2,4,5] => [3,-2,4,5,1] => ? = 8 - 1
[1,2,-4,3,5] => [5,3,-4,2,1] => [1,3,-2,4,5] => [-3,2,4,5,-1] => ? = 7 - 1
[1,2,-4,3,-5] => [-5,3,-4,2,1] => [-1,3,-2,4,5] => [-3,2,4,5,1] => ? = 6 - 1
[1,2,-4,-3,5] => [5,-3,-4,2,1] => [1,-3,-2,4,5] => [-3,-2,4,5,-1] => ? = 8 - 1
[1,2,-4,-3,-5] => [-5,-3,-4,2,1] => [-1,-3,-2,4,5] => [-3,-2,4,5,1] => ? = 7 - 1
[1,-2,4,3,5] => [5,3,4,-2,1] => [1,3,2,-4,5] => [3,2,-4,5,-1] => ? = 7 - 1
[1,-2,4,3,-5] => [-5,3,4,-2,1] => [-1,3,2,-4,5] => [3,2,-4,5,1] => ? = 6 - 1
[1,-2,4,-3,5] => [5,-3,4,-2,1] => [1,-3,2,-4,5] => [3,-2,-4,5,-1] => ? = 8 - 1
[1,-2,4,-3,-5] => [-5,-3,4,-2,1] => [-1,-3,2,-4,5] => [3,-2,-4,5,1] => ? = 7 - 1
[1,-2,-4,3,5] => [5,3,-4,-2,1] => [1,3,-2,-4,5] => [-3,2,-4,5,-1] => ? = 6 - 1
[1,-2,-4,3,-5] => [-5,3,-4,-2,1] => [-1,3,-2,-4,5] => [-3,2,-4,5,1] => ? = 5 - 1
[1,-2,-4,-3,5] => [5,-3,-4,-2,1] => [1,-3,-2,-4,5] => [-3,-2,-4,5,-1] => ? = 7 - 1
[1,-2,-4,-3,-5] => [-5,-3,-4,-2,1] => [-1,-3,-2,-4,5] => [-3,-2,-4,5,1] => ? = 6 - 1
[-1,2,4,3,5] => [5,3,4,2,-1] => [1,3,2,4,-5] => [3,2,4,-5,-1] => ? = 7 - 1
[-1,2,4,3,-5] => [-5,3,4,2,-1] => [-1,3,2,4,-5] => [3,2,4,-5,1] => ? = 6 - 1
Description
The flag excedance statistic of a signed permutation. This is the number of negative entries plus twice the number of excedances of the signed permutation. That is, fexc(σ)=2exc(σ)+neg(σ), where exc(σ)=|{i∈[n−1]:σ(i)>i}| neg(σ)=|{i∈[n]:σ(i)<0}| It has the same distribution as the flag descent statistic.