- FindStat

Identifier

St001425: Decorated permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [+]=>0
[-]=>1
[+,+]=>0
[-,+]=>1
[+,-]=>1
[-,-]=>2
[2,1]=>0
[+,+,+]=>0
[-,+,+]=>1
[+,-,+]=>1
[+,+,-]=>1
[-,-,+]=>2
[-,+,-]=>2
[+,-,-]=>2
[-,-,-]=>3
[+,3,2]=>0
[-,3,2]=>1
[2,1,+]=>0
[2,1,-]=>1
[2,3,1]=>0
[3,1,2]=>0
[3,+,1]=>0
[3,-,1]=>1
[+,+,+,+]=>0
[-,+,+,+]=>1
[+,-,+,+]=>1
[+,+,-,+]=>1
[+,+,+,-]=>1
[-,-,+,+]=>2
[-,+,-,+]=>2
[-,+,+,-]=>2
[+,-,-,+]=>2
[+,-,+,-]=>2
[+,+,-,-]=>2
[-,-,-,+]=>3
[-,-,+,-]=>3
[-,+,-,-]=>3
[+,-,-,-]=>3
[-,-,-,-]=>4
[+,+,4,3]=>0
[-,+,4,3]=>1
[+,-,4,3]=>1
[-,-,4,3]=>2
[+,3,2,+]=>0
[-,3,2,+]=>1
[+,3,2,-]=>1
[-,3,2,-]=>2
[+,3,4,2]=>0
[-,3,4,2]=>1
[+,4,2,3]=>0
[-,4,2,3]=>1
[+,4,+,2]=>0
[-,4,+,2]=>1
[+,4,-,2]=>1
[-,4,-,2]=>2
[2,1,+,+]=>0
[2,1,-,+]=>1
[2,1,+,-]=>1
[2,1,-,-]=>2
[2,1,4,3]=>0
[2,3,1,+]=>0
[2,3,1,-]=>1
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,+,1]=>0
[2,4,-,1]=>1
[3,1,2,+]=>0
[3,1,2,-]=>1
[3,1,4,2]=>0
[3,+,1,+]=>0
[3,-,1,+]=>1
[3,+,1,-]=>1
[3,-,1,-]=>2
[3,+,4,1]=>0
[3,-,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,+,2]=>0
[4,1,-,2]=>1
[4,+,1,3]=>0
[4,-,1,3]=>1
[4,+,+,1]=>0
[4,-,+,1]=>1
[4,+,-,1]=>1
[4,-,-,1]=>2
[4,3,1,2]=>0
[4,3,2,1]=>0
[+,+,+,+,+]=>0
[-,+,+,+,+]=>1
[+,-,+,+,+]=>1
[+,+,-,+,+]=>1
[+,+,+,-,+]=>1
[+,+,+,+,-]=>1
[-,-,+,+,+]=>2
[-,+,-,+,+]=>2
[-,+,+,-,+]=>2
[-,+,+,+,-]=>2
[+,-,-,+,+]=>2
[+,-,+,-,+]=>2
[+,-,+,+,-]=>2
[+,+,-,-,+]=>2
[+,+,-,+,-]=>2
[+,+,+,-,-]=>2
[-,-,-,+,+]=>3
[-,-,+,-,+]=>3
[-,-,+,+,-]=>3
[-,+,-,-,+]=>3
[-,+,-,+,-]=>3
[-,+,+,-,-]=>3
[+,-,-,-,+]=>3
[+,-,-,+,-]=>3
[+,-,+,-,-]=>3
[+,+,-,-,-]=>3
[-,-,-,-,+]=>4
[-,-,-,+,-]=>4
[-,-,+,-,-]=>4
[-,+,-,-,-]=>4
[+,-,-,-,-]=>4
[-,-,-,-,-]=>5
[+,+,+,5,4]=>0
[-,+,+,5,4]=>1
[+,-,+,5,4]=>1
[+,+,-,5,4]=>1
[-,-,+,5,4]=>2
[-,+,-,5,4]=>2
[+,-,-,5,4]=>2
[-,-,-,5,4]=>3
[+,+,4,3,+]=>0
[-,+,4,3,+]=>1
[+,-,4,3,+]=>1
[+,+,4,3,-]=>1
[-,-,4,3,+]=>2
[-,+,4,3,-]=>2
[+,-,4,3,-]=>2
[-,-,4,3,-]=>3
[+,+,4,5,3]=>0
[-,+,4,5,3]=>1
[+,-,4,5,3]=>1
[-,-,4,5,3]=>2
[+,+,5,3,4]=>0
[-,+,5,3,4]=>1
[+,-,5,3,4]=>1
[-,-,5,3,4]=>2
[+,+,5,+,3]=>0
[-,+,5,+,3]=>1
[+,-,5,+,3]=>1
[+,+,5,-,3]=>1
[-,-,5,+,3]=>2
[-,+,5,-,3]=>2
[+,-,5,-,3]=>2
[-,-,5,-,3]=>3
[+,3,2,+,+]=>0
[-,3,2,+,+]=>1
[+,3,2,-,+]=>1
[+,3,2,+,-]=>1
[-,3,2,-,+]=>2
[-,3,2,+,-]=>2
[+,3,2,-,-]=>2
[-,3,2,-,-]=>3
[+,3,2,5,4]=>0
[-,3,2,5,4]=>1
[+,3,4,2,+]=>0
[-,3,4,2,+]=>1
[+,3,4,2,-]=>1
[-,3,4,2,-]=>2
[+,3,4,5,2]=>0
[-,3,4,5,2]=>1
[+,3,5,2,4]=>0
[-,3,5,2,4]=>1
[+,3,5,+,2]=>0
[-,3,5,+,2]=>1
[+,3,5,-,2]=>1
[-,3,5,-,2]=>2
[+,4,2,3,+]=>0
[-,4,2,3,+]=>1
[+,4,2,3,-]=>1
[-,4,2,3,-]=>2
[+,4,2,5,3]=>0
[-,4,2,5,3]=>1
[+,4,+,2,+]=>0
[-,4,+,2,+]=>1
[+,4,-,2,+]=>1
[+,4,+,2,-]=>1
[-,4,-,2,+]=>2
[-,4,+,2,-]=>2
[+,4,-,2,-]=>2
[-,4,-,2,-]=>3
[+,4,+,5,2]=>0
[-,4,+,5,2]=>1
[+,4,-,5,2]=>1
[-,4,-,5,2]=>2
[+,4,5,2,3]=>0
[-,4,5,2,3]=>1
[+,4,5,3,2]=>0
[-,4,5,3,2]=>1
[+,5,2,3,4]=>0
[-,5,2,3,4]=>1
[+,5,2,+,3]=>0
[-,5,2,+,3]=>1
[+,5,2,-,3]=>1
[-,5,2,-,3]=>2
[+,5,+,2,4]=>0
[-,5,+,2,4]=>1
[+,5,-,2,4]=>1
[-,5,-,2,4]=>2
[+,5,+,+,2]=>0
[-,5,+,+,2]=>1
[+,5,-,+,2]=>1
[+,5,+,-,2]=>1
[-,5,-,+,2]=>2
[-,5,+,-,2]=>2
[+,5,-,-,2]=>2
[-,5,-,-,2]=>3
[+,5,4,2,3]=>0
[-,5,4,2,3]=>1
[+,5,4,3,2]=>0
[-,5,4,3,2]=>1
[2,1,+,+,+]=>0
[2,1,-,+,+]=>1
[2,1,+,-,+]=>1
[2,1,+,+,-]=>1
[2,1,-,-,+]=>2
[2,1,-,+,-]=>2
[2,1,+,-,-]=>2
[2,1,-,-,-]=>3
[2,1,+,5,4]=>0
[2,1,-,5,4]=>1
[2,1,4,3,+]=>0
[2,1,4,3,-]=>1
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,+,3]=>0
[2,1,5,-,3]=>1
[2,3,1,+,+]=>0
[2,3,1,-,+]=>1
[2,3,1,+,-]=>1
[2,3,1,-,-]=>2
[2,3,1,5,4]=>0
[2,3,4,1,+]=>0
[2,3,4,1,-]=>1
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,+,1]=>0
[2,3,5,-,1]=>1
[2,4,1,3,+]=>0
[2,4,1,3,-]=>1
[2,4,1,5,3]=>0
[2,4,+,1,+]=>0
[2,4,-,1,+]=>1
[2,4,+,1,-]=>1
[2,4,-,1,-]=>2
[2,4,+,5,1]=>0
[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]=>0
[2,5,1,-,3]=>1
[2,5,+,1,4]=>0
[2,5,-,1,4]=>1
[2,5,+,+,1]=>0
[2,5,-,+,1]=>1
[2,5,+,-,1]=>1
[2,5,-,-,1]=>2
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,+,+]=>0
[3,1,2,-,+]=>1
[3,1,2,+,-]=>1
[3,1,2,-,-]=>2
[3,1,2,5,4]=>0
[3,1,4,2,+]=>0
[3,1,4,2,-]=>1
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,+,2]=>0
[3,1,5,-,2]=>1
[3,+,1,+,+]=>0
[3,-,1,+,+]=>1
[3,+,1,-,+]=>1
[3,+,1,+,-]=>1
[3,-,1,-,+]=>2
[3,-,1,+,-]=>2
[3,+,1,-,-]=>2
[3,-,1,-,-]=>3
[3,+,1,5,4]=>0
[3,-,1,5,4]=>1
[3,+,4,1,+]=>0
[3,-,4,1,+]=>1
[3,+,4,1,-]=>1
[3,-,4,1,-]=>2
[3,+,4,5,1]=>0
[3,-,4,5,1]=>1
[3,+,5,1,4]=>0
[3,-,5,1,4]=>1
[3,+,5,+,1]=>0
[3,-,5,+,1]=>1
[3,+,5,-,1]=>1
[3,-,5,-,1]=>2
[3,4,1,2,+]=>0
[3,4,1,2,-]=>1
[3,4,1,5,2]=>0
[3,4,2,1,+]=>0
[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]=>0
[3,5,1,-,2]=>1
[3,5,2,1,4]=>0
[3,5,2,+,1]=>0
[3,5,2,-,1]=>1
[3,5,4,1,2]=>0
[3,5,4,2,1]=>0
[4,1,2,3,+]=>0
[4,1,2,3,-]=>1
[4,1,2,5,3]=>0
[4,1,+,2,+]=>0
[4,1,-,2,+]=>1
[4,1,+,2,-]=>1
[4,1,-,2,-]=>2
[4,1,+,5,2]=>0
[4,1,-,5,2]=>1
[4,1,5,2,3]=>0
[4,1,5,3,2]=>0
[4,+,1,3,+]=>0
[4,-,1,3,+]=>1
[4,+,1,3,-]=>1
[4,-,1,3,-]=>2
[4,+,1,5,3]=>0
[4,-,1,5,3]=>1
[4,+,+,1,+]=>0
[4,-,+,1,+]=>1
[4,+,-,1,+]=>1
[4,+,+,1,-]=>1
[4,-,-,1,+]=>2
[4,-,+,1,-]=>2
[4,+,-,1,-]=>2
[4,-,-,1,-]=>3
[4,+,+,5,1]=>0
[4,-,+,5,1]=>1
[4,+,-,5,1]=>1
[4,-,-,5,1]=>2
[4,+,5,1,3]=>0
[4,-,5,1,3]=>1
[4,+,5,3,1]=>0
[4,-,5,3,1]=>1
[4,3,1,2,+]=>0
[4,3,1,2,-]=>1
[4,3,1,5,2]=>0
[4,3,2,1,+]=>0
[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]=>0
[4,5,-,1,2]=>1
[4,5,+,2,1]=>0
[4,5,-,2,1]=>1
[5,1,2,3,4]=>0
[5,1,2,+,3]=>0
[5,1,2,-,3]=>1
[5,1,+,2,4]=>0
[5,1,-,2,4]=>1
[5,1,+,+,2]=>0
[5,1,-,+,2]=>1
[5,1,+,-,2]=>1
[5,1,-,-,2]=>2
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,+,1,3,4]=>0
[5,-,1,3,4]=>1
[5,+,1,+,3]=>0
[5,-,1,+,3]=>1
[5,+,1,-,3]=>1
[5,-,1,-,3]=>2
[5,+,+,1,4]=>0
[5,-,+,1,4]=>1
[5,+,-,1,4]=>1
[5,-,-,1,4]=>2
[5,+,+,+,1]=>0
[5,-,+,+,1]=>1
[5,+,-,+,1]=>1
[5,+,+,-,1]=>1
[5,-,-,+,1]=>2
[5,-,+,-,1]=>2
[5,+,-,-,1]=>2
[5,-,-,-,1]=>3
[5,+,4,1,3]=>0
[5,-,4,1,3]=>1
[5,+,4,3,1]=>0
[5,-,4,3,1]=>1
[5,3,1,2,4]=>0
[5,3,1,+,2]=>0
[5,3,1,-,2]=>1
[5,3,2,1,4]=>0
[5,3,2,+,1]=>0
[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]=>0
[5,4,-,1,2]=>1
[5,4,+,2,1]=>0
[5,4,-,2,1]=>1
                    

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Description

The number of negatively decorated fixed points of a decorated permutation.

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)
    return sum(1 for i in as_permutation(pi).fixed_points() if tau[i-1] < 0)

Created

Jun 20, 2019 at 08:00 by Christian Stump

Updated

Jun 20, 2019 at 08:00 by Christian Stump