Identifier
Identifier
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
click to show generating function       
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