Identifier
Values
=>
[+,+]=>0
[-,+]=>0
[+,-]=>1
[-,-]=>0
[2,1]=>0
[+,+,+]=>0
[-,+,+]=>0
[+,-,+]=>1
[+,+,-]=>2
[-,-,+]=>0
[-,+,-]=>1
[+,-,-]=>2
[-,-,-]=>0
[+,3,2]=>1
[-,3,2]=>0
[2,1,+]=>0
[2,1,-]=>1
[2,3,1]=>0
[3,1,2]=>0
[3,+,1]=>1
[3,-,1]=>1
[+,+,+,+]=>0
[-,+,+,+]=>0
[+,-,+,+]=>1
[+,+,-,+]=>2
[+,+,+,-]=>3
[-,-,+,+]=>0
[-,+,-,+]=>1
[-,+,+,-]=>2
[+,-,-,+]=>2
[+,-,+,-]=>3
[+,+,-,-]=>4
[-,-,-,+]=>0
[-,-,+,-]=>1
[-,+,-,-]=>2
[+,-,-,-]=>3
[-,-,-,-]=>0
[+,+,4,3]=>2
[-,+,4,3]=>1
[+,-,4,3]=>2
[-,-,4,3]=>0
[+,3,2,+]=>1
[-,3,2,+]=>0
[+,3,2,-]=>3
[-,3,2,-]=>1
[+,3,4,2]=>2
[-,3,4,2]=>0
[+,4,2,3]=>1
[-,4,2,3]=>0
[+,4,+,2]=>2
[-,4,+,2]=>1
[+,4,-,2]=>3
[-,4,-,2]=>1
[2,1,+,+]=>0
[2,1,-,+]=>1
[2,1,+,-]=>2
[2,1,-,-]=>2
[2,1,4,3]=>1
[2,3,1,+]=>0
[2,3,1,-]=>1
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,+,1]=>1
[2,4,-,1]=>1
[3,1,2,+]=>0
[3,1,2,-]=>2
[3,1,4,2]=>1
[3,+,1,+]=>1
[3,-,1,+]=>1
[3,+,1,-]=>3
[3,-,1,-]=>2
[3,+,4,1]=>2
[3,-,4,1]=>1
[3,4,1,2]=>0
[3,4,2,1]=>1
[4,1,2,3]=>0
[4,1,+,2]=>1
[4,1,-,2]=>2
[4,+,1,3]=>1
[4,-,1,3]=>1
[4,+,+,1]=>2
[4,-,+,1]=>2
[4,+,-,1]=>3
[4,-,-,1]=>2
[4,3,1,2]=>1
[4,3,2,1]=>2
[+,+,+,+,+]=>0
[-,+,+,+,+]=>0
[+,-,+,+,+]=>1
[+,+,-,+,+]=>2
[+,+,+,-,+]=>3
[+,+,+,+,-]=>4
[-,-,+,+,+]=>0
[-,+,-,+,+]=>1
[-,+,+,-,+]=>2
[-,+,+,+,-]=>3
[+,-,-,+,+]=>2
[+,-,+,-,+]=>3
[+,-,+,+,-]=>4
[+,+,-,-,+]=>4
[+,+,-,+,-]=>5
[+,+,+,-,-]=>6
[-,-,-,+,+]=>0
[-,-,+,-,+]=>1
[-,-,+,+,-]=>2
[-,+,-,-,+]=>2
[-,+,-,+,-]=>3
[-,+,+,-,-]=>4
[+,-,-,-,+]=>3
[+,-,-,+,-]=>4
[+,-,+,-,-]=>5
[+,+,-,-,-]=>6
[-,-,-,-,+]=>0
[-,-,-,+,-]=>1
[-,-,+,-,-]=>2
[-,+,-,-,-]=>3
[+,-,-,-,-]=>4
[-,-,-,-,-]=>0
[+,+,+,5,4]=>3
[-,+,+,5,4]=>2
[+,-,+,5,4]=>3
[+,+,-,5,4]=>4
[-,-,+,5,4]=>1
[-,+,-,5,4]=>2
[+,-,-,5,4]=>3
[-,-,-,5,4]=>0
[+,+,4,3,+]=>2
[-,+,4,3,+]=>1
[+,-,4,3,+]=>2
[+,+,4,3,-]=>5
[-,-,4,3,+]=>0
[-,+,4,3,-]=>3
[+,-,4,3,-]=>4
[-,-,4,3,-]=>1
[+,+,4,5,3]=>4
[-,+,4,5,3]=>2
[+,-,4,5,3]=>3
[-,-,4,5,3]=>0
[+,+,5,3,4]=>2
[-,+,5,3,4]=>1
[+,-,5,3,4]=>2
[-,-,5,3,4]=>0
[+,+,5,+,3]=>3
[-,+,5,+,3]=>2
[+,-,5,+,3]=>3
[+,+,5,-,3]=>5
[-,-,5,+,3]=>1
[-,+,5,-,3]=>3
[+,-,5,-,3]=>4
[-,-,5,-,3]=>1
[+,3,2,+,+]=>1
[-,3,2,+,+]=>0
[+,3,2,-,+]=>3
[+,3,2,+,-]=>4
[-,3,2,-,+]=>1
[-,3,2,+,-]=>2
[+,3,2,-,-]=>5
[-,3,2,-,-]=>2
[+,3,2,5,4]=>3
[-,3,2,5,4]=>1
[+,3,4,2,+]=>2
[-,3,4,2,+]=>0
[+,3,4,2,-]=>4
[-,3,4,2,-]=>1
[+,3,4,5,2]=>3
[-,3,4,5,2]=>0
[+,3,5,2,4]=>2
[-,3,5,2,4]=>0
[+,3,5,+,2]=>3
[-,3,5,+,2]=>1
[+,3,5,-,2]=>4
[-,3,5,-,2]=>1
[+,4,2,3,+]=>1
[-,4,2,3,+]=>0
[+,4,2,3,-]=>4
[-,4,2,3,-]=>2
[+,4,2,5,3]=>3
[-,4,2,5,3]=>1
[+,4,+,2,+]=>2
[-,4,+,2,+]=>1
[+,4,-,2,+]=>3
[+,4,+,2,-]=>5
[-,4,-,2,+]=>1
[-,4,+,2,-]=>3
[+,4,-,2,-]=>5
[-,4,-,2,-]=>2
[+,4,+,5,2]=>4
[-,4,+,5,2]=>2
[+,4,-,5,2]=>4
[-,4,-,5,2]=>1
[+,4,5,2,3]=>2
[-,4,5,2,3]=>0
[+,4,5,3,2]=>3
[-,4,5,3,2]=>1
[+,5,2,3,4]=>1
[-,5,2,3,4]=>0
[+,5,2,+,3]=>2
[-,5,2,+,3]=>1
[+,5,2,-,3]=>4
[-,5,2,-,3]=>2
[+,5,+,2,4]=>2
[-,5,+,2,4]=>1
[+,5,-,2,4]=>3
[-,5,-,2,4]=>1
[+,5,+,+,2]=>3
[-,5,+,+,2]=>2
[+,5,-,+,2]=>4
[+,5,+,-,2]=>5
[-,5,-,+,2]=>2
[-,5,+,-,2]=>3
[+,5,-,-,2]=>5
[-,5,-,-,2]=>2
[+,5,4,2,3]=>3
[-,5,4,2,3]=>1
[+,5,4,3,2]=>4
[-,5,4,3,2]=>2
[2,1,+,+,+]=>0
[2,1,-,+,+]=>1
[2,1,+,-,+]=>2
[2,1,+,+,-]=>3
[2,1,-,-,+]=>2
[2,1,-,+,-]=>3
[2,1,+,-,-]=>4
[2,1,-,-,-]=>3
[2,1,+,5,4]=>2
[2,1,-,5,4]=>2
[2,1,4,3,+]=>1
[2,1,4,3,-]=>3
[2,1,4,5,3]=>2
[2,1,5,3,4]=>1
[2,1,5,+,3]=>2
[2,1,5,-,3]=>3
[2,3,1,+,+]=>0
[2,3,1,-,+]=>1
[2,3,1,+,-]=>2
[2,3,1,-,-]=>2
[2,3,1,5,4]=>1
[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]=>1
[2,3,5,-,1]=>1
[2,4,1,3,+]=>0
[2,4,1,3,-]=>2
[2,4,1,5,3]=>1
[2,4,+,1,+]=>1
[2,4,-,1,+]=>1
[2,4,+,1,-]=>3
[2,4,-,1,-]=>2
[2,4,+,5,1]=>2
[2,4,-,5,1]=>1
[2,4,5,1,3]=>0
[2,4,5,3,1]=>1
[2,5,1,3,4]=>0
[2,5,1,+,3]=>1
[2,5,1,-,3]=>2
[2,5,+,1,4]=>1
[2,5,-,1,4]=>1
[2,5,+,+,1]=>2
[2,5,-,+,1]=>2
[2,5,+,-,1]=>3
[2,5,-,-,1]=>2
[2,5,4,1,3]=>1
[2,5,4,3,1]=>2
[3,1,2,+,+]=>0
[3,1,2,-,+]=>2
[3,1,2,+,-]=>3
[3,1,2,-,-]=>4
[3,1,2,5,4]=>2
[3,1,4,2,+]=>1
[3,1,4,2,-]=>3
[3,1,4,5,2]=>2
[3,1,5,2,4]=>1
[3,1,5,+,2]=>2
[3,1,5,-,2]=>3
[3,+,1,+,+]=>1
[3,-,1,+,+]=>1
[3,+,1,-,+]=>3
[3,+,1,+,-]=>4
[3,-,1,-,+]=>2
[3,-,1,+,-]=>3
[3,+,1,-,-]=>5
[3,-,1,-,-]=>3
[3,+,1,5,4]=>3
[3,-,1,5,4]=>2
[3,+,4,1,+]=>2
[3,-,4,1,+]=>1
[3,+,4,1,-]=>4
[3,-,4,1,-]=>2
[3,+,4,5,1]=>3
[3,-,4,5,1]=>1
[3,+,5,1,4]=>2
[3,-,5,1,4]=>1
[3,+,5,+,1]=>3
[3,-,5,+,1]=>2
[3,+,5,-,1]=>4
[3,-,5,-,1]=>2
[3,4,1,2,+]=>0
[3,4,1,2,-]=>2
[3,4,1,5,2]=>1
[3,4,2,1,+]=>1
[3,4,2,1,-]=>3
[3,4,2,5,1]=>2
[3,4,5,1,2]=>0
[3,4,5,2,1]=>1
[3,5,1,2,4]=>0
[3,5,1,+,2]=>1
[3,5,1,-,2]=>2
[3,5,2,1,4]=>1
[3,5,2,+,1]=>2
[3,5,2,-,1]=>3
[3,5,4,1,2]=>1
[3,5,4,2,1]=>2
[4,1,2,3,+]=>0
[4,1,2,3,-]=>3
[4,1,2,5,3]=>2
[4,1,+,2,+]=>1
[4,1,-,2,+]=>2
[4,1,+,2,-]=>4
[4,1,-,2,-]=>4
[4,1,+,5,2]=>3
[4,1,-,5,2]=>3
[4,1,5,2,3]=>1
[4,1,5,3,2]=>2
[4,+,1,3,+]=>1
[4,-,1,3,+]=>1
[4,+,1,3,-]=>4
[4,-,1,3,-]=>3
[4,+,1,5,3]=>3
[4,-,1,5,3]=>2
[4,+,+,1,+]=>2
[4,-,+,1,+]=>2
[4,+,-,1,+]=>3
[4,+,+,1,-]=>5
[4,-,-,1,+]=>2
[4,-,+,1,-]=>4
[4,+,-,1,-]=>5
[4,-,-,1,-]=>3
[4,+,+,5,1]=>4
[4,-,+,5,1]=>3
[4,+,-,5,1]=>4
[4,-,-,5,1]=>2
[4,+,5,1,3]=>2
[4,-,5,1,3]=>1
[4,+,5,3,1]=>3
[4,-,5,3,1]=>2
[4,3,1,2,+]=>1
[4,3,1,2,-]=>3
[4,3,1,5,2]=>2
[4,3,2,1,+]=>2
[4,3,2,1,-]=>4
[4,3,2,5,1]=>3
[4,3,5,1,2]=>1
[4,3,5,2,1]=>2
[4,5,1,2,3]=>0
[4,5,1,3,2]=>1
[4,5,2,1,3]=>1
[4,5,2,3,1]=>2
[4,5,+,1,2]=>2
[4,5,-,1,2]=>2
[4,5,+,2,1]=>3
[4,5,-,2,1]=>3
[5,1,2,3,4]=>0
[5,1,2,+,3]=>1
[5,1,2,-,3]=>3
[5,1,+,2,4]=>1
[5,1,-,2,4]=>2
[5,1,+,+,2]=>2
[5,1,-,+,2]=>3
[5,1,+,-,2]=>4
[5,1,-,-,2]=>4
[5,1,4,2,3]=>2
[5,1,4,3,2]=>3
[5,+,1,3,4]=>1
[5,-,1,3,4]=>1
[5,+,1,+,3]=>2
[5,-,1,+,3]=>2
[5,+,1,-,3]=>4
[5,-,1,-,3]=>3
[5,+,+,1,4]=>2
[5,-,+,1,4]=>2
[5,+,-,1,4]=>3
[5,-,-,1,4]=>2
[5,+,+,+,1]=>3
[5,-,+,+,1]=>3
[5,+,-,+,1]=>4
[5,+,+,-,1]=>5
[5,-,-,+,1]=>3
[5,-,+,-,1]=>4
[5,+,-,-,1]=>5
[5,-,-,-,1]=>3
[5,+,4,1,3]=>3
[5,-,4,1,3]=>2
[5,+,4,3,1]=>4
[5,-,4,3,1]=>3
[5,3,1,2,4]=>1
[5,3,1,+,2]=>2
[5,3,1,-,2]=>3
[5,3,2,1,4]=>2
[5,3,2,+,1]=>3
[5,3,2,-,1]=>4
[5,3,4,1,2]=>2
[5,3,4,2,1]=>3
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>2
[5,4,2,3,1]=>3
[5,4,+,1,2]=>3
[5,4,-,1,2]=>3
[5,4,+,2,1]=>4
[5,4,-,2,1]=>4
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Description
The inversion number of the associated bounded affine permutation.
The inversion number is given by $\ell(f) = |\{(i, j) \in [n] \times \mathbb Z \; | \; i < j \text{ and } f(i) > f(j)\}|$
The inversion number is given by $\ell(f) = |\{(i, j) \in [n] \times \mathbb Z \; | \; i < j \text{ and } f(i) > f(j)\}|$
References
[1] Lam, T. Totally nonnegative Grassmannian and Grassmann polytopes MathSciNet:3468251 arXiv:1506.00603
Code
def dectobap(pi):
bap=[]
tau = list(pi)
for j in range(0,len(tau)):
if tau[j]==(j+1):
bap.append(j+1+len(tau))
elif tau[j]<0:
bap.append(j+1)
else:
if tau[j]<(j+1):
add_n=tau[j]+len(tau)
bap.append(add_n)
else:
bap.append(tau[j])
return bap
def statistic(pi):
count=0
tau = dectobap(pi)
for i in range(0,len(tau)-1):
for j in range(i+1,len(tau)):
if tau[i]>tau[j]:
count += 1
return count
Created
May 12, 2020 at 22:38 by Danny Luecke
Updated
May 13, 2020 at 15:04 by Danny Luecke
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