Identifier
Values
=>
[+,+]=>0
[-,+]=>1
[+,-]=>2
[-,-]=>3
[2,1]=>1
[+,+,+]=>0
[-,+,+]=>1
[+,-,+]=>2
[+,+,-]=>3
[-,-,+]=>3
[-,+,-]=>4
[+,-,-]=>5
[-,-,-]=>6
[+,3,2]=>2
[-,3,2]=>3
[2,1,+]=>1
[2,1,-]=>4
[2,3,1]=>1
[3,1,2]=>3
[3,+,1]=>1
[3,-,1]=>3
[+,+,+,+]=>0
[-,+,+,+]=>1
[+,-,+,+]=>2
[+,+,-,+]=>3
[+,+,+,-]=>4
[-,-,+,+]=>3
[-,+,-,+]=>4
[-,+,+,-]=>5
[+,-,-,+]=>5
[+,-,+,-]=>6
[+,+,-,-]=>7
[-,-,-,+]=>6
[-,-,+,-]=>7
[-,+,-,-]=>8
[+,-,-,-]=>9
[-,-,-,-]=>10
[+,+,4,3]=>3
[-,+,4,3]=>4
[+,-,4,3]=>5
[-,-,4,3]=>6
[+,3,2,+]=>2
[-,3,2,+]=>3
[+,3,2,-]=>6
[-,3,2,-]=>7
[+,3,4,2]=>2
[-,3,4,2]=>3
[+,4,2,3]=>5
[-,4,2,3]=>6
[+,4,+,2]=>2
[-,4,+,2]=>3
[+,4,-,2]=>5
[-,4,-,2]=>6
[2,1,+,+]=>1
[2,1,-,+]=>4
[2,1,+,-]=>5
[2,1,-,-]=>8
[2,1,4,3]=>4
[2,3,1,+]=>1
[2,3,1,-]=>5
[2,3,4,1]=>1
[2,4,1,3]=>4
[2,4,+,1]=>1
[2,4,-,1]=>4
[3,1,2,+]=>3
[3,1,2,-]=>7
[3,1,4,2]=>3
[3,+,1,+]=>1
[3,-,1,+]=>3
[3,+,1,-]=>5
[3,-,1,-]=>7
[3,+,4,1]=>1
[3,-,4,1]=>3
[3,4,1,2]=>3
[3,4,2,1]=>3
[4,1,2,3]=>6
[4,1,+,2]=>3
[4,1,-,2]=>6
[4,+,1,3]=>4
[4,-,1,3]=>6
[4,+,+,1]=>1
[4,-,+,1]=>3
[4,+,-,1]=>4
[4,-,-,1]=>6
[4,3,1,2]=>3
[4,3,2,1]=>3
[+,+,+,+,+]=>0
[-,+,+,+,+]=>1
[+,-,+,+,+]=>2
[+,+,-,+,+]=>3
[+,+,+,-,+]=>4
[+,+,+,+,-]=>5
[-,-,+,+,+]=>3
[-,+,-,+,+]=>4
[-,+,+,-,+]=>5
[-,+,+,+,-]=>6
[+,-,-,+,+]=>5
[+,-,+,-,+]=>6
[+,-,+,+,-]=>7
[+,+,-,-,+]=>7
[+,+,-,+,-]=>8
[+,+,+,-,-]=>9
[-,-,-,+,+]=>6
[-,-,+,-,+]=>7
[-,-,+,+,-]=>8
[-,+,-,-,+]=>8
[-,+,-,+,-]=>9
[-,+,+,-,-]=>10
[+,-,-,-,+]=>9
[+,-,-,+,-]=>10
[+,-,+,-,-]=>11
[+,+,-,-,-]=>12
[-,-,-,-,+]=>10
[-,-,-,+,-]=>11
[-,-,+,-,-]=>12
[-,+,-,-,-]=>13
[+,-,-,-,-]=>14
[-,-,-,-,-]=>15
[+,+,+,5,4]=>4
[-,+,+,5,4]=>5
[+,-,+,5,4]=>6
[+,+,-,5,4]=>7
[-,-,+,5,4]=>7
[-,+,-,5,4]=>8
[+,-,-,5,4]=>9
[-,-,-,5,4]=>10
[+,+,4,3,+]=>3
[-,+,4,3,+]=>4
[+,-,4,3,+]=>5
[+,+,4,3,-]=>8
[-,-,4,3,+]=>6
[-,+,4,3,-]=>9
[+,-,4,3,-]=>10
[-,-,4,3,-]=>11
[+,+,4,5,3]=>3
[-,+,4,5,3]=>4
[+,-,4,5,3]=>5
[-,-,4,5,3]=>6
[+,+,5,3,4]=>7
[-,+,5,3,4]=>8
[+,-,5,3,4]=>9
[-,-,5,3,4]=>10
[+,+,5,+,3]=>3
[-,+,5,+,3]=>4
[+,-,5,+,3]=>5
[+,+,5,-,3]=>7
[-,-,5,+,3]=>6
[-,+,5,-,3]=>8
[+,-,5,-,3]=>9
[-,-,5,-,3]=>10
[+,3,2,+,+]=>2
[-,3,2,+,+]=>3
[+,3,2,-,+]=>6
[+,3,2,+,-]=>7
[-,3,2,-,+]=>7
[-,3,2,+,-]=>8
[+,3,2,-,-]=>11
[-,3,2,-,-]=>12
[+,3,2,5,4]=>6
[-,3,2,5,4]=>7
[+,3,4,2,+]=>2
[-,3,4,2,+]=>3
[+,3,4,2,-]=>7
[-,3,4,2,-]=>8
[+,3,4,5,2]=>2
[-,3,4,5,2]=>3
[+,3,5,2,4]=>6
[-,3,5,2,4]=>7
[+,3,5,+,2]=>2
[-,3,5,+,2]=>3
[+,3,5,-,2]=>6
[-,3,5,-,2]=>7
[+,4,2,3,+]=>5
[-,4,2,3,+]=>6
[+,4,2,3,-]=>10
[-,4,2,3,-]=>11
[+,4,2,5,3]=>5
[-,4,2,5,3]=>6
[+,4,+,2,+]=>2
[-,4,+,2,+]=>3
[+,4,-,2,+]=>5
[+,4,+,2,-]=>7
[-,4,-,2,+]=>6
[-,4,+,2,-]=>8
[+,4,-,2,-]=>10
[-,4,-,2,-]=>11
[+,4,+,5,2]=>2
[-,4,+,5,2]=>3
[+,4,-,5,2]=>5
[-,4,-,5,2]=>6
[+,4,5,2,3]=>5
[-,4,5,2,3]=>6
[+,4,5,3,2]=>5
[-,4,5,3,2]=>6
[+,5,2,3,4]=>9
[-,5,2,3,4]=>10
[+,5,2,+,3]=>5
[-,5,2,+,3]=>6
[+,5,2,-,3]=>9
[-,5,2,-,3]=>10
[+,5,+,2,4]=>6
[-,5,+,2,4]=>7
[+,5,-,2,4]=>9
[-,5,-,2,4]=>10
[+,5,+,+,2]=>2
[-,5,+,+,2]=>3
[+,5,-,+,2]=>5
[+,5,+,-,2]=>6
[-,5,-,+,2]=>6
[-,5,+,-,2]=>7
[+,5,-,-,2]=>9
[-,5,-,-,2]=>10
[+,5,4,2,3]=>5
[-,5,4,2,3]=>6
[+,5,4,3,2]=>5
[-,5,4,3,2]=>6
[2,1,+,+,+]=>1
[2,1,-,+,+]=>4
[2,1,+,-,+]=>5
[2,1,+,+,-]=>6
[2,1,-,-,+]=>8
[2,1,-,+,-]=>9
[2,1,+,-,-]=>10
[2,1,-,-,-]=>13
[2,1,+,5,4]=>5
[2,1,-,5,4]=>8
[2,1,4,3,+]=>4
[2,1,4,3,-]=>9
[2,1,4,5,3]=>4
[2,1,5,3,4]=>8
[2,1,5,+,3]=>4
[2,1,5,-,3]=>8
[2,3,1,+,+]=>1
[2,3,1,-,+]=>5
[2,3,1,+,-]=>6
[2,3,1,-,-]=>10
[2,3,1,5,4]=>5
[2,3,4,1,+]=>1
[2,3,4,1,-]=>6
[2,3,4,5,1]=>1
[2,3,5,1,4]=>5
[2,3,5,+,1]=>1
[2,3,5,-,1]=>5
[2,4,1,3,+]=>4
[2,4,1,3,-]=>9
[2,4,1,5,3]=>4
[2,4,+,1,+]=>1
[2,4,-,1,+]=>4
[2,4,+,1,-]=>6
[2,4,-,1,-]=>9
[2,4,+,5,1]=>1
[2,4,-,5,1]=>4
[2,4,5,1,3]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>8
[2,5,1,+,3]=>4
[2,5,1,-,3]=>8
[2,5,+,1,4]=>5
[2,5,-,1,4]=>8
[2,5,+,+,1]=>1
[2,5,-,+,1]=>4
[2,5,+,-,1]=>5
[2,5,-,-,1]=>8
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,+,+]=>3
[3,1,2,-,+]=>7
[3,1,2,+,-]=>8
[3,1,2,-,-]=>12
[3,1,2,5,4]=>7
[3,1,4,2,+]=>3
[3,1,4,2,-]=>8
[3,1,4,5,2]=>3
[3,1,5,2,4]=>7
[3,1,5,+,2]=>3
[3,1,5,-,2]=>7
[3,+,1,+,+]=>1
[3,-,1,+,+]=>3
[3,+,1,-,+]=>5
[3,+,1,+,-]=>6
[3,-,1,-,+]=>7
[3,-,1,+,-]=>8
[3,+,1,-,-]=>10
[3,-,1,-,-]=>12
[3,+,1,5,4]=>5
[3,-,1,5,4]=>7
[3,+,4,1,+]=>1
[3,-,4,1,+]=>3
[3,+,4,1,-]=>6
[3,-,4,1,-]=>8
[3,+,4,5,1]=>1
[3,-,4,5,1]=>3
[3,+,5,1,4]=>5
[3,-,5,1,4]=>7
[3,+,5,+,1]=>1
[3,-,5,+,1]=>3
[3,+,5,-,1]=>5
[3,-,5,-,1]=>7
[3,4,1,2,+]=>3
[3,4,1,2,-]=>8
[3,4,1,5,2]=>3
[3,4,2,1,+]=>3
[3,4,2,1,-]=>8
[3,4,2,5,1]=>3
[3,4,5,1,2]=>3
[3,4,5,2,1]=>3
[3,5,1,2,4]=>7
[3,5,1,+,2]=>3
[3,5,1,-,2]=>7
[3,5,2,1,4]=>7
[3,5,2,+,1]=>3
[3,5,2,-,1]=>7
[3,5,4,1,2]=>3
[3,5,4,2,1]=>3
[4,1,2,3,+]=>6
[4,1,2,3,-]=>11
[4,1,2,5,3]=>6
[4,1,+,2,+]=>3
[4,1,-,2,+]=>6
[4,1,+,2,-]=>8
[4,1,-,2,-]=>11
[4,1,+,5,2]=>3
[4,1,-,5,2]=>6
[4,1,5,2,3]=>6
[4,1,5,3,2]=>6
[4,+,1,3,+]=>4
[4,-,1,3,+]=>6
[4,+,1,3,-]=>9
[4,-,1,3,-]=>11
[4,+,1,5,3]=>4
[4,-,1,5,3]=>6
[4,+,+,1,+]=>1
[4,-,+,1,+]=>3
[4,+,-,1,+]=>4
[4,+,+,1,-]=>6
[4,-,-,1,+]=>6
[4,-,+,1,-]=>8
[4,+,-,1,-]=>9
[4,-,-,1,-]=>11
[4,+,+,5,1]=>1
[4,-,+,5,1]=>3
[4,+,-,5,1]=>4
[4,-,-,5,1]=>6
[4,+,5,1,3]=>4
[4,-,5,1,3]=>6
[4,+,5,3,1]=>4
[4,-,5,3,1]=>6
[4,3,1,2,+]=>3
[4,3,1,2,-]=>8
[4,3,1,5,2]=>3
[4,3,2,1,+]=>3
[4,3,2,1,-]=>8
[4,3,2,5,1]=>3
[4,3,5,1,2]=>3
[4,3,5,2,1]=>3
[4,5,1,2,3]=>6
[4,5,1,3,2]=>6
[4,5,2,1,3]=>6
[4,5,2,3,1]=>6
[4,5,+,1,2]=>3
[4,5,-,1,2]=>6
[4,5,+,2,1]=>3
[4,5,-,2,1]=>6
[5,1,2,3,4]=>10
[5,1,2,+,3]=>6
[5,1,2,-,3]=>10
[5,1,+,2,4]=>7
[5,1,-,2,4]=>10
[5,1,+,+,2]=>3
[5,1,-,+,2]=>6
[5,1,+,-,2]=>7
[5,1,-,-,2]=>10
[5,1,4,2,3]=>6
[5,1,4,3,2]=>6
[5,+,1,3,4]=>8
[5,-,1,3,4]=>10
[5,+,1,+,3]=>4
[5,-,1,+,3]=>6
[5,+,1,-,3]=>8
[5,-,1,-,3]=>10
[5,+,+,1,4]=>5
[5,-,+,1,4]=>7
[5,+,-,1,4]=>8
[5,-,-,1,4]=>10
[5,+,+,+,1]=>1
[5,-,+,+,1]=>3
[5,+,-,+,1]=>4
[5,+,+,-,1]=>5
[5,-,-,+,1]=>6
[5,-,+,-,1]=>7
[5,+,-,-,1]=>8
[5,-,-,-,1]=>10
[5,+,4,1,3]=>4
[5,-,4,1,3]=>6
[5,+,4,3,1]=>4
[5,-,4,3,1]=>6
[5,3,1,2,4]=>7
[5,3,1,+,2]=>3
[5,3,1,-,2]=>7
[5,3,2,1,4]=>7
[5,3,2,+,1]=>3
[5,3,2,-,1]=>7
[5,3,4,1,2]=>3
[5,3,4,2,1]=>3
[5,4,1,2,3]=>6
[5,4,1,3,2]=>6
[5,4,2,1,3]=>6
[5,4,2,3,1]=>6
[5,4,+,1,2]=>3
[5,4,-,1,2]=>6
[5,4,+,2,1]=>3
[5,4,-,2,1]=>6
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The sum of the indices of the first term of the associated Grassmann necklace.
Here, we use Postnikov's map (p.59) from decorated permutations to Grassmann necklaces.
Here, we use Postnikov's map (p.59) from decorated permutations to Grassmann necklaces.
References
[1] A. Postnikov, Total positivity, Grassmannians, and networks. 27 Sep 2006. Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def dectoneck(pi):
tau=list(pi)
n=len(tau)
perm=[]
neck=[ [] for _ in range(n) ]
for j in range(0,n):
if tau[j]<0:
for k in range(0,n):
neck[k].append(abs(tau[j]))
perm.append(abs(tau[j]))
perminv=Permutation(perm).inverse()
for el in range(1,n+1):
adjust_index=[]
adjust_perminv=[]
for m in range(0,n):
if el>(m+1):
adjust_index.append(m+1+n)
else:
adjust_index.append(m+1)
if el>perminv[m]:
adjust_perminv.append(perminv[m]+n)
else:
adjust_perminv.append(perminv[m])
for x in range(0,n):
if adjust_index[x] < adjust_perminv[x]:
neck[el-1].append(x+1)
for y in range(0,n):
neck[y].sort()
return neck
def statistic(pi):
tau=dectoneck(pi)
sum=0
for i in range(0,len(tau[0])):
sum = sum + tau[0][i]
return sum
Created
May 14, 2020 at 20:46 by Danny Luecke
Updated
May 14, 2020 at 22:05 by Danny Luecke
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!