Identifier
Values
=>
[+]=>1
[-]=>0
[+,+]=>2
[-,+]=>1
[+,-]=>1
[-,-]=>0
[2,1]=>1
[+,+,+]=>3
[-,+,+]=>2
[+,-,+]=>2
[+,+,-]=>2
[-,-,+]=>1
[-,+,-]=>1
[+,-,-]=>1
[-,-,-]=>0
[+,3,2]=>2
[-,3,2]=>1
[2,1,+]=>2
[2,1,-]=>1
[2,3,1]=>2
[3,1,2]=>1
[3,+,1]=>2
[3,-,1]=>1
[+,+,+,+]=>4
[-,+,+,+]=>3
[+,-,+,+]=>3
[+,+,-,+]=>3
[+,+,+,-]=>3
[-,-,+,+]=>2
[-,+,-,+]=>2
[-,+,+,-]=>2
[+,-,-,+]=>2
[+,-,+,-]=>2
[+,+,-,-]=>2
[-,-,-,+]=>1
[-,-,+,-]=>1
[-,+,-,-]=>1
[+,-,-,-]=>1
[-,-,-,-]=>0
[+,+,4,3]=>3
[-,+,4,3]=>2
[+,-,4,3]=>2
[-,-,4,3]=>1
[+,3,2,+]=>3
[-,3,2,+]=>2
[+,3,2,-]=>2
[-,3,2,-]=>1
[+,3,4,2]=>3
[-,3,4,2]=>2
[+,4,2,3]=>2
[-,4,2,3]=>1
[+,4,+,2]=>3
[-,4,+,2]=>2
[+,4,-,2]=>2
[-,4,-,2]=>1
[2,1,+,+]=>3
[2,1,-,+]=>2
[2,1,+,-]=>2
[2,1,-,-]=>1
[2,1,4,3]=>2
[2,3,1,+]=>3
[2,3,1,-]=>2
[2,3,4,1]=>3
[2,4,1,3]=>2
[2,4,+,1]=>3
[2,4,-,1]=>2
[3,1,2,+]=>2
[3,1,2,-]=>1
[3,1,4,2]=>2
[3,+,1,+]=>3
[3,-,1,+]=>2
[3,+,1,-]=>2
[3,-,1,-]=>1
[3,+,4,1]=>3
[3,-,4,1]=>2
[3,4,1,2]=>2
[3,4,2,1]=>2
[4,1,2,3]=>1
[4,1,+,2]=>2
[4,1,-,2]=>1
[4,+,1,3]=>2
[4,-,1,3]=>1
[4,+,+,1]=>3
[4,-,+,1]=>2
[4,+,-,1]=>2
[4,-,-,1]=>1
[4,3,1,2]=>2
[4,3,2,1]=>2
[+,+,+,+,+]=>5
[-,+,+,+,+]=>4
[+,-,+,+,+]=>4
[+,+,-,+,+]=>4
[+,+,+,-,+]=>4
[+,+,+,+,-]=>4
[-,-,+,+,+]=>3
[-,+,-,+,+]=>3
[-,+,+,-,+]=>3
[-,+,+,+,-]=>3
[+,-,-,+,+]=>3
[+,-,+,-,+]=>3
[+,-,+,+,-]=>3
[+,+,-,-,+]=>3
[+,+,-,+,-]=>3
[+,+,+,-,-]=>3
[-,-,-,+,+]=>2
[-,-,+,-,+]=>2
[-,-,+,+,-]=>2
[-,+,-,-,+]=>2
[-,+,-,+,-]=>2
[-,+,+,-,-]=>2
[+,-,-,-,+]=>2
[+,-,-,+,-]=>2
[+,-,+,-,-]=>2
[+,+,-,-,-]=>2
[-,-,-,-,+]=>1
[-,-,-,+,-]=>1
[-,-,+,-,-]=>1
[-,+,-,-,-]=>1
[+,-,-,-,-]=>1
[-,-,-,-,-]=>0
[+,+,+,5,4]=>4
[-,+,+,5,4]=>3
[+,-,+,5,4]=>3
[+,+,-,5,4]=>3
[-,-,+,5,4]=>2
[-,+,-,5,4]=>2
[+,-,-,5,4]=>2
[-,-,-,5,4]=>1
[+,+,4,3,+]=>4
[-,+,4,3,+]=>3
[+,-,4,3,+]=>3
[+,+,4,3,-]=>3
[-,-,4,3,+]=>2
[-,+,4,3,-]=>2
[+,-,4,3,-]=>2
[-,-,4,3,-]=>1
[+,+,4,5,3]=>4
[-,+,4,5,3]=>3
[+,-,4,5,3]=>3
[-,-,4,5,3]=>2
[+,+,5,3,4]=>3
[-,+,5,3,4]=>2
[+,-,5,3,4]=>2
[-,-,5,3,4]=>1
[+,+,5,+,3]=>4
[-,+,5,+,3]=>3
[+,-,5,+,3]=>3
[+,+,5,-,3]=>3
[-,-,5,+,3]=>2
[-,+,5,-,3]=>2
[+,-,5,-,3]=>2
[-,-,5,-,3]=>1
[+,3,2,+,+]=>4
[-,3,2,+,+]=>3
[+,3,2,-,+]=>3
[+,3,2,+,-]=>3
[-,3,2,-,+]=>2
[-,3,2,+,-]=>2
[+,3,2,-,-]=>2
[-,3,2,-,-]=>1
[+,3,2,5,4]=>3
[-,3,2,5,4]=>2
[+,3,4,2,+]=>4
[-,3,4,2,+]=>3
[+,3,4,2,-]=>3
[-,3,4,2,-]=>2
[+,3,4,5,2]=>4
[-,3,4,5,2]=>3
[+,3,5,2,4]=>3
[-,3,5,2,4]=>2
[+,3,5,+,2]=>4
[-,3,5,+,2]=>3
[+,3,5,-,2]=>3
[-,3,5,-,2]=>2
[+,4,2,3,+]=>3
[-,4,2,3,+]=>2
[+,4,2,3,-]=>2
[-,4,2,3,-]=>1
[+,4,2,5,3]=>3
[-,4,2,5,3]=>2
[+,4,+,2,+]=>4
[-,4,+,2,+]=>3
[+,4,-,2,+]=>3
[+,4,+,2,-]=>3
[-,4,-,2,+]=>2
[-,4,+,2,-]=>2
[+,4,-,2,-]=>2
[-,4,-,2,-]=>1
[+,4,+,5,2]=>4
[-,4,+,5,2]=>3
[+,4,-,5,2]=>3
[-,4,-,5,2]=>2
[+,4,5,2,3]=>3
[-,4,5,2,3]=>2
[+,4,5,3,2]=>3
[-,4,5,3,2]=>2
[+,5,2,3,4]=>2
[-,5,2,3,4]=>1
[+,5,2,+,3]=>3
[-,5,2,+,3]=>2
[+,5,2,-,3]=>2
[-,5,2,-,3]=>1
[+,5,+,2,4]=>3
[-,5,+,2,4]=>2
[+,5,-,2,4]=>2
[-,5,-,2,4]=>1
[+,5,+,+,2]=>4
[-,5,+,+,2]=>3
[+,5,-,+,2]=>3
[+,5,+,-,2]=>3
[-,5,-,+,2]=>2
[-,5,+,-,2]=>2
[+,5,-,-,2]=>2
[-,5,-,-,2]=>1
[+,5,4,2,3]=>3
[-,5,4,2,3]=>2
[+,5,4,3,2]=>3
[-,5,4,3,2]=>2
[2,1,+,+,+]=>4
[2,1,-,+,+]=>3
[2,1,+,-,+]=>3
[2,1,+,+,-]=>3
[2,1,-,-,+]=>2
[2,1,-,+,-]=>2
[2,1,+,-,-]=>2
[2,1,-,-,-]=>1
[2,1,+,5,4]=>3
[2,1,-,5,4]=>2
[2,1,4,3,+]=>3
[2,1,4,3,-]=>2
[2,1,4,5,3]=>3
[2,1,5,3,4]=>2
[2,1,5,+,3]=>3
[2,1,5,-,3]=>2
[2,3,1,+,+]=>4
[2,3,1,-,+]=>3
[2,3,1,+,-]=>3
[2,3,1,-,-]=>2
[2,3,1,5,4]=>3
[2,3,4,1,+]=>4
[2,3,4,1,-]=>3
[2,3,4,5,1]=>4
[2,3,5,1,4]=>3
[2,3,5,+,1]=>4
[2,3,5,-,1]=>3
[2,4,1,3,+]=>3
[2,4,1,3,-]=>2
[2,4,1,5,3]=>3
[2,4,+,1,+]=>4
[2,4,-,1,+]=>3
[2,4,+,1,-]=>3
[2,4,-,1,-]=>2
[2,4,+,5,1]=>4
[2,4,-,5,1]=>3
[2,4,5,1,3]=>3
[2,4,5,3,1]=>3
[2,5,1,3,4]=>2
[2,5,1,+,3]=>3
[2,5,1,-,3]=>2
[2,5,+,1,4]=>3
[2,5,-,1,4]=>2
[2,5,+,+,1]=>4
[2,5,-,+,1]=>3
[2,5,+,-,1]=>3
[2,5,-,-,1]=>2
[2,5,4,1,3]=>3
[2,5,4,3,1]=>3
[3,1,2,+,+]=>3
[3,1,2,-,+]=>2
[3,1,2,+,-]=>2
[3,1,2,-,-]=>1
[3,1,2,5,4]=>2
[3,1,4,2,+]=>3
[3,1,4,2,-]=>2
[3,1,4,5,2]=>3
[3,1,5,2,4]=>2
[3,1,5,+,2]=>3
[3,1,5,-,2]=>2
[3,+,1,+,+]=>4
[3,-,1,+,+]=>3
[3,+,1,-,+]=>3
[3,+,1,+,-]=>3
[3,-,1,-,+]=>2
[3,-,1,+,-]=>2
[3,+,1,-,-]=>2
[3,-,1,-,-]=>1
[3,+,1,5,4]=>3
[3,-,1,5,4]=>2
[3,+,4,1,+]=>4
[3,-,4,1,+]=>3
[3,+,4,1,-]=>3
[3,-,4,1,-]=>2
[3,+,4,5,1]=>4
[3,-,4,5,1]=>3
[3,+,5,1,4]=>3
[3,-,5,1,4]=>2
[3,+,5,+,1]=>4
[3,-,5,+,1]=>3
[3,+,5,-,1]=>3
[3,-,5,-,1]=>2
[3,4,1,2,+]=>3
[3,4,1,2,-]=>2
[3,4,1,5,2]=>3
[3,4,2,1,+]=>3
[3,4,2,1,-]=>2
[3,4,2,5,1]=>3
[3,4,5,1,2]=>3
[3,4,5,2,1]=>3
[3,5,1,2,4]=>2
[3,5,1,+,2]=>3
[3,5,1,-,2]=>2
[3,5,2,1,4]=>2
[3,5,2,+,1]=>3
[3,5,2,-,1]=>2
[3,5,4,1,2]=>3
[3,5,4,2,1]=>3
[4,1,2,3,+]=>2
[4,1,2,3,-]=>1
[4,1,2,5,3]=>2
[4,1,+,2,+]=>3
[4,1,-,2,+]=>2
[4,1,+,2,-]=>2
[4,1,-,2,-]=>1
[4,1,+,5,2]=>3
[4,1,-,5,2]=>2
[4,1,5,2,3]=>2
[4,1,5,3,2]=>2
[4,+,1,3,+]=>3
[4,-,1,3,+]=>2
[4,+,1,3,-]=>2
[4,-,1,3,-]=>1
[4,+,1,5,3]=>3
[4,-,1,5,3]=>2
[4,+,+,1,+]=>4
[4,-,+,1,+]=>3
[4,+,-,1,+]=>3
[4,+,+,1,-]=>3
[4,-,-,1,+]=>2
[4,-,+,1,-]=>2
[4,+,-,1,-]=>2
[4,-,-,1,-]=>1
[4,+,+,5,1]=>4
[4,-,+,5,1]=>3
[4,+,-,5,1]=>3
[4,-,-,5,1]=>2
[4,+,5,1,3]=>3
[4,-,5,1,3]=>2
[4,+,5,3,1]=>3
[4,-,5,3,1]=>2
[4,3,1,2,+]=>3
[4,3,1,2,-]=>2
[4,3,1,5,2]=>3
[4,3,2,1,+]=>3
[4,3,2,1,-]=>2
[4,3,2,5,1]=>3
[4,3,5,1,2]=>3
[4,3,5,2,1]=>3
[4,5,1,2,3]=>2
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>2
[4,5,+,1,2]=>3
[4,5,-,1,2]=>2
[4,5,+,2,1]=>3
[4,5,-,2,1]=>2
[5,1,2,3,4]=>1
[5,1,2,+,3]=>2
[5,1,2,-,3]=>1
[5,1,+,2,4]=>2
[5,1,-,2,4]=>1
[5,1,+,+,2]=>3
[5,1,-,+,2]=>2
[5,1,+,-,2]=>2
[5,1,-,-,2]=>1
[5,1,4,2,3]=>2
[5,1,4,3,2]=>2
[5,+,1,3,4]=>2
[5,-,1,3,4]=>1
[5,+,1,+,3]=>3
[5,-,1,+,3]=>2
[5,+,1,-,3]=>2
[5,-,1,-,3]=>1
[5,+,+,1,4]=>3
[5,-,+,1,4]=>2
[5,+,-,1,4]=>2
[5,-,-,1,4]=>1
[5,+,+,+,1]=>4
[5,-,+,+,1]=>3
[5,+,-,+,1]=>3
[5,+,+,-,1]=>3
[5,-,-,+,1]=>2
[5,-,+,-,1]=>2
[5,+,-,-,1]=>2
[5,-,-,-,1]=>1
[5,+,4,1,3]=>3
[5,-,4,1,3]=>2
[5,+,4,3,1]=>3
[5,-,4,3,1]=>2
[5,3,1,2,4]=>2
[5,3,1,+,2]=>3
[5,3,1,-,2]=>2
[5,3,2,1,4]=>2
[5,3,2,+,1]=>3
[5,3,2,-,1]=>2
[5,3,4,1,2]=>3
[5,3,4,2,1]=>3
[5,4,1,2,3]=>2
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>2
[5,4,+,1,2]=>3
[5,4,-,1,2]=>2
[5,4,+,2,1]=>3
[5,4,-,2,1]=>2
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Description
The number of weak exceedances of a decorated permutation.
A weak exceedance of a decorated permutation $\tau$ is a position $i$ such that $i > \tau(i)$ or $i = \tau(i)$ and $\tau(i)$ has positive decoration.
A weak exceedance of a decorated permutation $\tau$ is a position $i$ such that $i > \tau(i)$ or $i = \tau(i)$ and $\tau(i)$ has positive decoration.
Code
def DecoratedPermutations(n):
for sigma in Permutations(n):
F = sigma.fixed_points()
for X in Subsets(F):
tau = list(sigma)
for i in X:
tau[i-1] = -tau[i-1]
yield list(SignedPermutations(n)(tau))
def element_repr(pi):
pi = list(pi)
for i,a in enumerate(pi):
if a == i+1:
pi[i] = 0
elif -a == i+1:
pi[i] = -1
return str(pi).replace(" ","").replace("0","+").replace("-1","-")
def statistic(d):
e = 0
for i in range(len(d)):
if d[i] >= i+1:
e += 1
return e
Created
Jul 15, 2020 at 15:35 by Dylan Heuer
Updated
Jul 15, 2020 at 15:35 by Dylan Heuer
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