- FindStat

Identifier

St001426: Decorated permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The number of positively 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 07:59 by Christian Stump

Updated

Jun 20, 2019 at 07:59 by Christian Stump