Identifier
Identifier
Values
[+,+] => 3
[-,+] => 1
[+,-] => -1
[-,-] => -3
[2,1] => 0
[+,+,+] => 6
[-,+,+] => 4
[+,-,+] => 2
[+,+,-] => 0
[-,-,+] => 0
[-,+,-] => -2
[+,-,-] => -4
[-,-,-] => -6
[+,3,2] => 1
[-,3,2] => -1
[2,1,+] => 3
[2,1,-] => -3
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 2
[3,-,1] => -2
[+,+,+,+] => 10
[-,+,+,+] => 8
[+,-,+,+] => 6
[+,+,-,+] => 4
[+,+,+,-] => 2
[-,-,+,+] => 4
[-,+,-,+] => 2
[-,+,+,-] => 0
[+,-,-,+] => 0
[+,-,+,-] => -2
[+,+,-,-] => -4
[-,-,-,+] => -2
[-,-,+,-] => -4
[-,+,-,-] => -6
[+,-,-,-] => -8
[-,-,-,-] => -10
[+,+,4,3] => 3
[-,+,4,3] => 1
[+,-,4,3] => -1
[-,-,4,3] => -3
[+,3,2,+] => 5
[-,3,2,+] => 3
[+,3,2,-] => -3
[-,3,2,-] => -5
[+,3,4,2] => 1
[-,3,4,2] => -1
[+,4,2,3] => 1
[-,4,2,3] => -1
[+,4,+,2] => 4
[-,4,+,2] => 2
[+,4,-,2] => -2
[-,4,-,2] => -4
[2,1,+,+] => 7
[2,1,-,+] => 1
[2,1,+,-] => -1
[2,1,-,-] => -7
[2,1,4,3] => 0
[2,3,1,+] => 4
[2,3,1,-] => -4
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,+,1] => 3
[2,4,-,1] => -3
[3,1,2,+] => 4
[3,1,2,-] => -4
[3,1,4,2] => 0
[3,+,1,+] => 6
[3,-,1,+] => 2
[3,+,1,-] => -2
[3,-,1,-] => -6
[3,+,4,1] => 2
[3,-,4,1] => -2
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,+,2] => 3
[4,1,-,2] => -3
[4,+,1,3] => 2
[4,-,1,3] => -2
[4,+,+,1] => 5
[4,-,+,1] => 1
[4,+,-,1] => -1
[4,-,-,1] => -5
[4,3,1,2] => 0
[4,3,2,1] => 0
[+,+,+,+,+] => 15
[-,+,+,+,+] => 13
[+,-,+,+,+] => 11
[+,+,-,+,+] => 9
[+,+,+,-,+] => 7
[+,+,+,+,-] => 5
[-,-,+,+,+] => 9
[-,+,-,+,+] => 7
[-,+,+,-,+] => 5
[-,+,+,+,-] => 3
[+,-,-,+,+] => 5
[+,-,+,-,+] => 3
[+,-,+,+,-] => 1
[+,+,-,-,+] => 1
[+,+,-,+,-] => -1
[+,+,+,-,-] => -3
[-,-,-,+,+] => 3
[-,-,+,-,+] => 1
[-,-,+,+,-] => -1
[-,+,-,-,+] => -1
[-,+,-,+,-] => -3
[-,+,+,-,-] => -5
[+,-,-,-,+] => -3
[+,-,-,+,-] => -5
[+,-,+,-,-] => -7
[+,+,-,-,-] => -9
[-,-,-,-,+] => -5
[-,-,-,+,-] => -7
[-,-,+,-,-] => -9
[-,+,-,-,-] => -11
[+,-,-,-,-] => -13
[-,-,-,-,-] => -15
[+,+,+,5,4] => 6
[-,+,+,5,4] => 4
[+,-,+,5,4] => 2
[+,+,-,5,4] => 0
[-,-,+,5,4] => 0
[-,+,-,5,4] => -2
[+,-,-,5,4] => -4
[-,-,-,5,4] => -6
[+,+,4,3,+] => 8
[-,+,4,3,+] => 6
[+,-,4,3,+] => 4
[+,+,4,3,-] => -2
[-,-,4,3,+] => 2
[-,+,4,3,-] => -4
[+,-,4,3,-] => -6
[-,-,4,3,-] => -8
[+,+,4,5,3] => 3
[-,+,4,5,3] => 1
[+,-,4,5,3] => -1
[-,-,4,5,3] => -3
[+,+,5,3,4] => 3
[-,+,5,3,4] => 1
[+,-,5,3,4] => -1
[-,-,5,3,4] => -3
[+,+,5,+,3] => 7
[-,+,5,+,3] => 5
[+,-,5,+,3] => 3
[+,+,5,-,3] => -1
[-,-,5,+,3] => 1
[-,+,5,-,3] => -3
[+,-,5,-,3] => -5
[-,-,5,-,3] => -7
[+,3,2,+,+] => 10
[-,3,2,+,+] => 8
[+,3,2,-,+] => 2
[+,3,2,+,-] => 0
[-,3,2,-,+] => 0
[-,3,2,+,-] => -2
[+,3,2,-,-] => -8
[-,3,2,-,-] => -10
[+,3,2,5,4] => 1
[-,3,2,5,4] => -1
[+,3,4,2,+] => 6
[-,3,4,2,+] => 4
[+,3,4,2,-] => -4
[-,3,4,2,-] => -6
[+,3,4,5,2] => 1
[-,3,4,5,2] => -1
[+,3,5,2,4] => 1
[-,3,5,2,4] => -1
[+,3,5,+,2] => 5
[-,3,5,+,2] => 3
[+,3,5,-,2] => -3
[-,3,5,-,2] => -5
[+,4,2,3,+] => 6
[-,4,2,3,+] => 4
[+,4,2,3,-] => -4
[-,4,2,3,-] => -6
[+,4,2,5,3] => 1
[-,4,2,5,3] => -1
[+,4,+,2,+] => 9
[-,4,+,2,+] => 7
[+,4,-,2,+] => 3
[+,4,+,2,-] => -1
[-,4,-,2,+] => 1
[-,4,+,2,-] => -3
[+,4,-,2,-] => -7
[-,4,-,2,-] => -9
[+,4,+,5,2] => 4
[-,4,+,5,2] => 2
[+,4,-,5,2] => -2
[-,4,-,5,2] => -4
[+,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] => 5
[-,5,2,+,3] => 3
[+,5,2,-,3] => -3
[-,5,2,-,3] => -5
[+,5,+,2,4] => 4
[-,5,+,2,4] => 2
[+,5,-,2,4] => -2
[-,5,-,2,4] => -4
[+,5,+,+,2] => 8
[-,5,+,+,2] => 6
[+,5,-,+,2] => 2
[+,5,+,-,2] => 0
[-,5,-,+,2] => 0
[-,5,+,-,2] => -2
[+,5,-,-,2] => -6
[-,5,-,-,2] => -8
[+,5,4,2,3] => 1
[-,5,4,2,3] => -1
[+,5,4,3,2] => 1
[-,5,4,3,2] => -1
[2,1,+,+,+] => 12
[2,1,-,+,+] => 6
[2,1,+,-,+] => 4
[2,1,+,+,-] => 2
[2,1,-,-,+] => -2
[2,1,-,+,-] => -4
[2,1,+,-,-] => -6
[2,1,-,-,-] => -12
[2,1,+,5,4] => 3
[2,1,-,5,4] => -3
[2,1,4,3,+] => 5
[2,1,4,3,-] => -5
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,+,3] => 4
[2,1,5,-,3] => -4
[2,3,1,+,+] => 9
[2,3,1,-,+] => 1
[2,3,1,+,-] => -1
[2,3,1,-,-] => -9
[2,3,1,5,4] => 0
[2,3,4,1,+] => 5
[2,3,4,1,-] => -5
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,+,1] => 4
[2,3,5,-,1] => -4
[2,4,1,3,+] => 5
[2,4,1,3,-] => -5
[2,4,1,5,3] => 0
[2,4,+,1,+] => 8
[2,4,-,1,+] => 2
[2,4,+,1,-] => -2
[2,4,-,1,-] => -8
[2,4,+,5,1] => 3
[2,4,-,5,1] => -3
[2,4,5,1,3] => 0
[2,4,5,3,1] => 0
[2,5,1,3,4] => 0
[2,5,1,+,3] => 4
[2,5,1,-,3] => -4
[2,5,+,1,4] => 3
[2,5,-,1,4] => -3
[2,5,+,+,1] => 7
[2,5,-,+,1] => 1
[2,5,+,-,1] => -1
[2,5,-,-,1] => -7
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,+,+] => 9
[3,1,2,-,+] => 1
[3,1,2,+,-] => -1
[3,1,2,-,-] => -9
[3,1,2,5,4] => 0
[3,1,4,2,+] => 5
[3,1,4,2,-] => -5
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,+,2] => 4
[3,1,5,-,2] => -4
[3,+,1,+,+] => 11
[3,-,1,+,+] => 7
[3,+,1,-,+] => 3
[3,+,1,+,-] => 1
[3,-,1,-,+] => -1
[3,-,1,+,-] => -3
[3,+,1,-,-] => -7
[3,-,1,-,-] => -11
[3,+,1,5,4] => 2
[3,-,1,5,4] => -2
[3,+,4,1,+] => 7
[3,-,4,1,+] => 3
[3,+,4,1,-] => -3
[3,-,4,1,-] => -7
[3,+,4,5,1] => 2
[3,-,4,5,1] => -2
[3,+,5,1,4] => 2
[3,-,5,1,4] => -2
[3,+,5,+,1] => 6
[3,-,5,+,1] => 2
[3,+,5,-,1] => -2
[3,-,5,-,1] => -6
[3,4,1,2,+] => 5
[3,4,1,2,-] => -5
[3,4,1,5,2] => 0
[3,4,2,1,+] => 5
[3,4,2,1,-] => -5
[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] => 4
[3,5,1,-,2] => -4
[3,5,2,1,4] => 0
[3,5,2,+,1] => 4
[3,5,2,-,1] => -4
[3,5,4,1,2] => 0
[3,5,4,2,1] => 0
[4,1,2,3,+] => 5
[4,1,2,3,-] => -5
[4,1,2,5,3] => 0
[4,1,+,2,+] => 8
[4,1,-,2,+] => 2
[4,1,+,2,-] => -2
[4,1,-,2,-] => -8
[4,1,+,5,2] => 3
[4,1,-,5,2] => -3
[4,1,5,2,3] => 0
[4,1,5,3,2] => 0
[4,+,1,3,+] => 7
[4,-,1,3,+] => 3
[4,+,1,3,-] => -3
[4,-,1,3,-] => -7
[4,+,1,5,3] => 2
[4,-,1,5,3] => -2
[4,+,+,1,+] => 10
[4,-,+,1,+] => 6
[4,+,-,1,+] => 4
[4,+,+,1,-] => 0
[4,-,-,1,+] => 0
[4,-,+,1,-] => -4
[4,+,-,1,-] => -6
[4,-,-,1,-] => -10
[4,+,+,5,1] => 5
[4,-,+,5,1] => 1
[4,+,-,5,1] => -1
[4,-,-,5,1] => -5
[4,+,5,1,3] => 2
[4,-,5,1,3] => -2
[4,+,5,3,1] => 2
[4,-,5,3,1] => -2
[4,3,1,2,+] => 5
[4,3,1,2,-] => -5
[4,3,1,5,2] => 0
[4,3,2,1,+] => 5
[4,3,2,1,-] => -5
[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] => 3
[4,5,-,1,2] => -3
[4,5,+,2,1] => 3
[4,5,-,2,1] => -3
[5,1,2,3,4] => 0
[5,1,2,+,3] => 4
[5,1,2,-,3] => -4
[5,1,+,2,4] => 3
[5,1,-,2,4] => -3
[5,1,+,+,2] => 7
[5,1,-,+,2] => 1
[5,1,+,-,2] => -1
[5,1,-,-,2] => -7
[5,1,4,2,3] => 0
[5,1,4,3,2] => 0
[5,+,1,3,4] => 2
[5,-,1,3,4] => -2
[5,+,1,+,3] => 6
[5,-,1,+,3] => 2
[5,+,1,-,3] => -2
[5,-,1,-,3] => -6
[5,+,+,1,4] => 5
[5,-,+,1,4] => 1
[5,+,-,1,4] => -1
[5,-,-,1,4] => -5
[5,+,+,+,1] => 9
[5,-,+,+,1] => 5
[5,+,-,+,1] => 3
[5,+,+,-,1] => 1
[5,-,-,+,1] => -1
[5,-,+,-,1] => -3
[5,+,-,-,1] => -5
[5,-,-,-,1] => -9
[5,+,4,1,3] => 2
[5,-,4,1,3] => -2
[5,+,4,3,1] => 2
[5,-,4,3,1] => -2
[5,3,1,2,4] => 0
[5,3,1,+,2] => 4
[5,3,1,-,2] => -4
[5,3,2,1,4] => 0
[5,3,2,+,1] => 4
[5,3,2,-,1] => -4
[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] => 3
[5,4,-,1,2] => -3
[5,4,+,2,1] => 3
[5,4,-,2,1] => -3
click to show generating function       
Description
Sum of decorated fixed points as signed integers.
Every fixed point decorated with a '+' is treated as a positive integer, and every fixed point decorated with a '-' is treated as a negative integer.
Code
def fixed_points_with_signs(pi):
    pi = list(pi)
    tau = []
    for i,a in enumerate(pi):
        if i+1==abs(a):
            tau.append(pi[i])
    return tau

def statistic(pi):
    return sum(list(fixed_points_with_signs(pi)))
Created
May 11, 2020 at 18:39 by James Thorne
Updated
May 11, 2020 at 18:39 by James Thorne