- FindStat

Identifier

St001540: Decorated permutations ⟶ ℤ

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
[+,+,+,-,-]=>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