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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001821
St001821: 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] => 3
[-1,2] => 1
[-1,-2] => 4
[2,1] => 1
[2,-1] => 2
[-2,1] => 3
[-2,-1] => 2
[1,2,3] => 0
[1,2,-3] => 5
[1,-2,3] => 3
[1,-2,-3] => 8
[-1,2,3] => 1
[-1,2,-3] => 6
[-1,-2,3] => 4
[-1,-2,-3] => 9
[1,3,2] => 1
[1,3,-2] => 4
[1,-3,2] => 7
[1,-3,-2] => 4
[-1,3,2] => 2
[-1,3,-2] => 5
[-1,-3,2] => 8
[-1,-3,-2] => 5
[2,1,3] => 1
[2,1,-3] => 6
[2,-1,3] => 2
[2,-1,-3] => 7
[-2,1,3] => 3
[-2,1,-3] => 8
[-2,-1,3] => 2
[-2,-1,-3] => 7
[2,3,1] => 2
[2,3,-1] => 3
[2,-3,1] => 6
[2,-3,-1] => 5
[-2,3,1] => 4
[-2,3,-1] => 3
[-2,-3,1] => 6
[-2,-3,-1] => 7
[3,1,2] => 3
[3,1,-2] => 5
[3,-1,2] => 4
[3,-1,-2] => 4
[-3,1,2] => 6
[-3,1,-2] => 4
[-3,-1,2] => 5
[-3,-1,-2] => 5
Description
The sorting index of a signed permutation. A signed permutation σ=[σ(1),,σ(n)] can be sorted [1,,n] by signed transpositions in the following way: First move ±n to its position and swap the sign if needed, then ±(n1),±(n2) and so on. For example for [2,4,5,1,3] we have the swaps [2,4,5,1,3][2,4,3,1,5][2,1,3,4,5][2,1,3,4,5][1,2,3,4,5] given by the signed transpositions (3,5),(2,4),(3,3),(1,2). If (i1,j1),,(in,jn) is the decomposition of σ obtained this way (including trivial transpositions) then the sorting index of σ is defined as sorB(σ)=n1k=1jkikχ(ik<0), where χ(ik<0) is 1 if ik is negative and 0 otherwise. For σ=[2,4,5,1,3] we have sorB(σ)=(53)+(4(2)1)+(3(3)1)+(21)=13.