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Identifier
Values
[+,+] => 2
[-,+] => 0
[+,-] => 0
[-,-] => 2
[2,1] => 0
[+,+,+] => 3
[-,+,+] => 1
[+,-,+] => 1
[+,+,-] => 1
[-,-,+] => 1
[-,+,-] => 1
[+,-,-] => 1
[-,-,-] => 3
[+,3,2] => 1
[-,3,2] => 1
[2,1,+] => 1
[2,1,-] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 1
[3,-,1] => 1
[+,+,+,+] => 4
[-,+,+,+] => 2
[+,-,+,+] => 2
[+,+,-,+] => 2
[+,+,+,-] => 2
[-,-,+,+] => 0
[-,+,-,+] => 0
[-,+,+,-] => 0
[+,-,-,+] => 0
[+,-,+,-] => 0
[+,+,-,-] => 0
[-,-,-,+] => 2
[-,-,+,-] => 2
[-,+,-,-] => 2
[+,-,-,-] => 2
[-,-,-,-] => 4
[+,+,4,3] => 2
[-,+,4,3] => 0
[+,-,4,3] => 0
[-,-,4,3] => 2
[+,3,2,+] => 2
[-,3,2,+] => 0
[+,3,2,-] => 0
[-,3,2,-] => 2
[+,3,4,2] => 1
[-,3,4,2] => 1
[+,4,2,3] => 1
[-,4,2,3] => 1
[+,4,+,2] => 2
[-,4,+,2] => 0
[+,4,-,2] => 0
[-,4,-,2] => 2
[2,1,+,+] => 2
[2,1,-,+] => 0
[2,1,+,-] => 0
[2,1,-,-] => 2
[2,1,4,3] => 0
[2,3,1,+] => 1
[2,3,1,-] => 1
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,+,1] => 1
[2,4,-,1] => 1
[3,1,2,+] => 1
[3,1,2,-] => 1
[3,1,4,2] => 0
[3,+,1,+] => 2
[3,-,1,+] => 0
[3,+,1,-] => 0
[3,-,1,-] => 2
[3,+,4,1] => 1
[3,-,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,+,2] => 1
[4,1,-,2] => 1
[4,+,1,3] => 1
[4,-,1,3] => 1
[4,+,+,1] => 2
[4,-,+,1] => 0
[4,+,-,1] => 0
[4,-,-,1] => 2
[4,3,1,2] => 0
[4,3,2,1] => 0
[+,+,+,+,+] => 5
[-,+,+,+,+] => 3
[+,-,+,+,+] => 3
[+,+,-,+,+] => 3
[+,+,+,-,+] => 3
[+,+,+,+,-] => 3
[-,-,+,+,+] => 1
[-,+,-,+,+] => 1
[-,+,+,-,+] => 1
[-,+,+,+,-] => 1
[+,-,-,+,+] => 1
[+,-,+,-,+] => 1
[+,-,+,+,-] => 1
[+,+,-,-,+] => 1
[+,+,-,+,-] => 1
>>> Load all 412 entries. <<<
[+,+,+,-,-] => 1
[-,-,-,+,+] => 1
[-,-,+,-,+] => 1
[-,-,+,+,-] => 1
[-,+,-,-,+] => 1
[-,+,-,+,-] => 1
[-,+,+,-,-] => 1
[+,-,-,-,+] => 1
[+,-,-,+,-] => 1
[+,-,+,-,-] => 1
[+,+,-,-,-] => 1
[-,-,-,-,+] => 3
[-,-,-,+,-] => 3
[-,-,+,-,-] => 3
[-,+,-,-,-] => 3
[+,-,-,-,-] => 3
[-,-,-,-,-] => 5
[+,+,+,5,4] => 3
[-,+,+,5,4] => 1
[+,-,+,5,4] => 1
[+,+,-,5,4] => 1
[-,-,+,5,4] => 1
[-,+,-,5,4] => 1
[+,-,-,5,4] => 1
[-,-,-,5,4] => 3
[+,+,4,3,+] => 3
[-,+,4,3,+] => 1
[+,-,4,3,+] => 1
[+,+,4,3,-] => 1
[-,-,4,3,+] => 1
[-,+,4,3,-] => 1
[+,-,4,3,-] => 1
[-,-,4,3,-] => 3
[+,+,4,5,3] => 2
[-,+,4,5,3] => 0
[+,-,4,5,3] => 0
[-,-,4,5,3] => 2
[+,+,5,3,4] => 2
[-,+,5,3,4] => 0
[+,-,5,3,4] => 0
[-,-,5,3,4] => 2
[+,+,5,+,3] => 3
[-,+,5,+,3] => 1
[+,-,5,+,3] => 1
[+,+,5,-,3] => 1
[-,-,5,+,3] => 1
[-,+,5,-,3] => 1
[+,-,5,-,3] => 1
[-,-,5,-,3] => 3
[+,3,2,+,+] => 3
[-,3,2,+,+] => 1
[+,3,2,-,+] => 1
[+,3,2,+,-] => 1
[-,3,2,-,+] => 1
[-,3,2,+,-] => 1
[+,3,2,-,-] => 1
[-,3,2,-,-] => 3
[+,3,2,5,4] => 1
[-,3,2,5,4] => 1
[+,3,4,2,+] => 2
[-,3,4,2,+] => 0
[+,3,4,2,-] => 0
[-,3,4,2,-] => 2
[+,3,4,5,2] => 1
[-,3,4,5,2] => 1
[+,3,5,2,4] => 1
[-,3,5,2,4] => 1
[+,3,5,+,2] => 2
[-,3,5,+,2] => 0
[+,3,5,-,2] => 0
[-,3,5,-,2] => 2
[+,4,2,3,+] => 2
[-,4,2,3,+] => 0
[+,4,2,3,-] => 0
[-,4,2,3,-] => 2
[+,4,2,5,3] => 1
[-,4,2,5,3] => 1
[+,4,+,2,+] => 3
[-,4,+,2,+] => 1
[+,4,-,2,+] => 1
[+,4,+,2,-] => 1
[-,4,-,2,+] => 1
[-,4,+,2,-] => 1
[+,4,-,2,-] => 1
[-,4,-,2,-] => 3
[+,4,+,5,2] => 2
[-,4,+,5,2] => 0
[+,4,-,5,2] => 0
[-,4,-,5,2] => 2
[+,4,5,2,3] => 1
[-,4,5,2,3] => 1
[+,4,5,3,2] => 1
[-,4,5,3,2] => 1
[+,5,2,3,4] => 1
[-,5,2,3,4] => 1
[+,5,2,+,3] => 2
[-,5,2,+,3] => 0
[+,5,2,-,3] => 0
[-,5,2,-,3] => 2
[+,5,+,2,4] => 2
[-,5,+,2,4] => 0
[+,5,-,2,4] => 0
[-,5,-,2,4] => 2
[+,5,+,+,2] => 3
[-,5,+,+,2] => 1
[+,5,-,+,2] => 1
[+,5,+,-,2] => 1
[-,5,-,+,2] => 1
[-,5,+,-,2] => 1
[+,5,-,-,2] => 1
[-,5,-,-,2] => 3
[+,5,4,2,3] => 1
[-,5,4,2,3] => 1
[+,5,4,3,2] => 1
[-,5,4,3,2] => 1
[2,1,+,+,+] => 3
[2,1,-,+,+] => 1
[2,1,+,-,+] => 1
[2,1,+,+,-] => 1
[2,1,-,-,+] => 1
[2,1,-,+,-] => 1
[2,1,+,-,-] => 1
[2,1,-,-,-] => 3
[2,1,+,5,4] => 1
[2,1,-,5,4] => 1
[2,1,4,3,+] => 1
[2,1,4,3,-] => 1
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,+,3] => 1
[2,1,5,-,3] => 1
[2,3,1,+,+] => 2
[2,3,1,-,+] => 0
[2,3,1,+,-] => 0
[2,3,1,-,-] => 2
[2,3,1,5,4] => 0
[2,3,4,1,+] => 1
[2,3,4,1,-] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,+,1] => 1
[2,3,5,-,1] => 1
[2,4,1,3,+] => 1
[2,4,1,3,-] => 1
[2,4,1,5,3] => 0
[2,4,+,1,+] => 2
[2,4,-,1,+] => 0
[2,4,+,1,-] => 0
[2,4,-,1,-] => 2
[2,4,+,5,1] => 1
[2,4,-,5,1] => 1
[2,4,5,1,3] => 0
[2,4,5,3,1] => 0
[2,5,1,3,4] => 0
[2,5,1,+,3] => 1
[2,5,1,-,3] => 1
[2,5,+,1,4] => 1
[2,5,-,1,4] => 1
[2,5,+,+,1] => 2
[2,5,-,+,1] => 0
[2,5,+,-,1] => 0
[2,5,-,-,1] => 2
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,+,+] => 2
[3,1,2,-,+] => 0
[3,1,2,+,-] => 0
[3,1,2,-,-] => 2
[3,1,2,5,4] => 0
[3,1,4,2,+] => 1
[3,1,4,2,-] => 1
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,+,2] => 1
[3,1,5,-,2] => 1
[3,+,1,+,+] => 3
[3,-,1,+,+] => 1
[3,+,1,-,+] => 1
[3,+,1,+,-] => 1
[3,-,1,-,+] => 1
[3,-,1,+,-] => 1
[3,+,1,-,-] => 1
[3,-,1,-,-] => 3
[3,+,1,5,4] => 1
[3,-,1,5,4] => 1
[3,+,4,1,+] => 2
[3,-,4,1,+] => 0
[3,+,4,1,-] => 0
[3,-,4,1,-] => 2
[3,+,4,5,1] => 1
[3,-,4,5,1] => 1
[3,+,5,1,4] => 1
[3,-,5,1,4] => 1
[3,+,5,+,1] => 2
[3,-,5,+,1] => 0
[3,+,5,-,1] => 0
[3,-,5,-,1] => 2
[3,4,1,2,+] => 1
[3,4,1,2,-] => 1
[3,4,1,5,2] => 0
[3,4,2,1,+] => 1
[3,4,2,1,-] => 1
[3,4,2,5,1] => 0
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 0
[3,5,1,+,2] => 1
[3,5,1,-,2] => 1
[3,5,2,1,4] => 0
[3,5,2,+,1] => 1
[3,5,2,-,1] => 1
[3,5,4,1,2] => 0
[3,5,4,2,1] => 0
[4,1,2,3,+] => 1
[4,1,2,3,-] => 1
[4,1,2,5,3] => 0
[4,1,+,2,+] => 2
[4,1,-,2,+] => 0
[4,1,+,2,-] => 0
[4,1,-,2,-] => 2
[4,1,+,5,2] => 1
[4,1,-,5,2] => 1
[4,1,5,2,3] => 0
[4,1,5,3,2] => 0
[4,+,1,3,+] => 2
[4,-,1,3,+] => 0
[4,+,1,3,-] => 0
[4,-,1,3,-] => 2
[4,+,1,5,3] => 1
[4,-,1,5,3] => 1
[4,+,+,1,+] => 3
[4,-,+,1,+] => 1
[4,+,-,1,+] => 1
[4,+,+,1,-] => 1
[4,-,-,1,+] => 1
[4,-,+,1,-] => 1
[4,+,-,1,-] => 1
[4,-,-,1,-] => 3
[4,+,+,5,1] => 2
[4,-,+,5,1] => 0
[4,+,-,5,1] => 0
[4,-,-,5,1] => 2
[4,+,5,1,3] => 1
[4,-,5,1,3] => 1
[4,+,5,3,1] => 1
[4,-,5,3,1] => 1
[4,3,1,2,+] => 1
[4,3,1,2,-] => 1
[4,3,1,5,2] => 0
[4,3,2,1,+] => 1
[4,3,2,1,-] => 1
[4,3,2,5,1] => 0
[4,3,5,1,2] => 0
[4,3,5,2,1] => 0
[4,5,1,2,3] => 0
[4,5,1,3,2] => 0
[4,5,2,1,3] => 0
[4,5,2,3,1] => 0
[4,5,+,1,2] => 1
[4,5,-,1,2] => 1
[4,5,+,2,1] => 1
[4,5,-,2,1] => 1
[5,1,2,3,4] => 0
[5,1,2,+,3] => 1
[5,1,2,-,3] => 1
[5,1,+,2,4] => 1
[5,1,-,2,4] => 1
[5,1,+,+,2] => 2
[5,1,-,+,2] => 0
[5,1,+,-,2] => 0
[5,1,-,-,2] => 2
[5,1,4,2,3] => 0
[5,1,4,3,2] => 0
[5,+,1,3,4] => 1
[5,-,1,3,4] => 1
[5,+,1,+,3] => 2
[5,-,1,+,3] => 0
[5,+,1,-,3] => 0
[5,-,1,-,3] => 2
[5,+,+,1,4] => 2
[5,-,+,1,4] => 0
[5,+,-,1,4] => 0
[5,-,-,1,4] => 2
[5,+,+,+,1] => 3
[5,-,+,+,1] => 1
[5,+,-,+,1] => 1
[5,+,+,-,1] => 1
[5,-,-,+,1] => 1
[5,-,+,-,1] => 1
[5,+,-,-,1] => 1
[5,-,-,-,1] => 3
[5,+,4,1,3] => 1
[5,-,4,1,3] => 1
[5,+,4,3,1] => 1
[5,-,4,3,1] => 1
[5,3,1,2,4] => 0
[5,3,1,+,2] => 1
[5,3,1,-,2] => 1
[5,3,2,1,4] => 0
[5,3,2,+,1] => 1
[5,3,2,-,1] => 1
[5,3,4,1,2] => 0
[5,3,4,2,1] => 0
[5,4,1,2,3] => 0
[5,4,1,3,2] => 0
[5,4,2,1,3] => 0
[5,4,2,3,1] => 0
[5,4,+,1,2] => 1
[5,4,-,1,2] => 1
[5,4,+,2,1] => 1
[5,4,-,2,1] => 1
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Description
Difference in positively decorated fixed points and negatively decorated fixed points.
Code
def as_permutation(pi):
    pi = list(pi)
    for i,a in enumerate(pi):
        if a < 0:
            pi[i] = -a
    return Permutation(pi)

def statistic(pi):
    tau = list(pi)
    pos = sum(1 for i in as_permutation(pi).fixed_points() if tau[i-1] > 0)
    neg = sum(1 for i in as_permutation(pi).fixed_points() if tau[i-1] < 0)
    return (pos-neg)
Created
May 11, 2020 at 03:21 by James Thorne
Updated
May 11, 2020 at 03:21 by James Thorne