Identifier
Values
=>
[+,+]=>0
[-,+]=>2
[+,-]=>4
[-,-]=>6
[2,1]=>3
[+,+,+]=>0
[-,+,+]=>3
[+,-,+]=>6
[+,+,-]=>9
[-,-,+]=>9
[-,+,-]=>12
[+,-,-]=>15
[-,-,-]=>18
[+,3,2]=>7
[-,3,2]=>10
[2,1,+]=>4
[2,1,-]=>13
[2,3,1]=>6
[3,1,2]=>12
[3,+,1]=>7
[3,-,1]=>13
[+,+,+,+]=>0
[-,+,+,+]=>4
[+,-,+,+]=>8
[+,+,-,+]=>12
[+,+,+,-]=>16
[-,-,+,+]=>12
[-,+,-,+]=>16
[-,+,+,-]=>20
[+,-,-,+]=>20
[+,-,+,-]=>24
[+,+,-,-]=>28
[-,-,-,+]=>24
[-,-,+,-]=>28
[-,+,-,-]=>32
[+,-,-,-]=>36
[-,-,-,-]=>40
[+,+,4,3]=>13
[-,+,4,3]=>17
[+,-,4,3]=>21
[-,-,4,3]=>25
[+,3,2,+]=>9
[-,3,2,+]=>13
[+,3,2,-]=>25
[-,3,2,-]=>29
[+,3,4,2]=>11
[-,3,4,2]=>15
[+,4,2,3]=>23
[-,4,2,3]=>27
[+,4,+,2]=>12
[-,4,+,2]=>16
[+,4,-,2]=>24
[-,4,-,2]=>28
[2,1,+,+]=>5
[2,1,-,+]=>17
[2,1,+,-]=>21
[2,1,-,-]=>33
[2,1,4,3]=>18
[2,3,1,+]=>7
[2,3,1,-]=>23
[2,3,4,1]=>10
[2,4,1,3]=>21
[2,4,+,1]=>11
[2,4,-,1]=>23
[3,1,2,+]=>15
[3,1,2,-]=>31
[3,1,4,2]=>17
[3,+,1,+]=>8
[3,-,1,+]=>16
[3,+,1,-]=>24
[3,-,1,-]=>32
[3,+,4,1]=>11
[3,-,4,1]=>19
[3,4,1,2]=>20
[3,4,2,1]=>21
[4,1,2,3]=>30
[4,1,+,2]=>19
[4,1,-,2]=>31
[4,+,1,3]=>23
[4,-,1,3]=>31
[4,+,+,1]=>13
[4,-,+,1]=>21
[4,+,-,1]=>25
[4,-,-,1]=>33
[4,3,1,2]=>21
[4,3,2,1]=>22
[+,+,+,+,+]=>0
[-,+,+,+,+]=>5
[+,-,+,+,+]=>10
[+,+,-,+,+]=>15
[+,+,+,-,+]=>20
[+,+,+,+,-]=>25
[-,-,+,+,+]=>15
[-,+,-,+,+]=>20
[-,+,+,-,+]=>25
[-,+,+,+,-]=>30
[+,-,-,+,+]=>25
[+,-,+,-,+]=>30
[+,-,+,+,-]=>35
[+,+,-,-,+]=>35
[+,+,-,+,-]=>40
[+,+,+,-,-]=>45
[-,-,-,+,+]=>30
[-,-,+,-,+]=>35
[-,-,+,+,-]=>40
[-,+,-,-,+]=>40
[-,+,-,+,-]=>45
[-,+,+,-,-]=>50
[+,-,-,-,+]=>45
[+,-,-,+,-]=>50
[+,-,+,-,-]=>55
[+,+,-,-,-]=>60
[-,-,-,-,+]=>50
[-,-,-,+,-]=>55
[-,-,+,-,-]=>60
[-,+,-,-,-]=>65
[+,-,-,-,-]=>70
[-,-,-,-,-]=>75
[+,+,+,5,4]=>21
[-,+,+,5,4]=>26
[+,-,+,5,4]=>31
[+,+,-,5,4]=>36
[-,-,+,5,4]=>36
[-,+,-,5,4]=>41
[+,-,-,5,4]=>46
[-,-,-,5,4]=>51
[+,+,4,3,+]=>16
[-,+,4,3,+]=>21
[+,-,4,3,+]=>26
[+,+,4,3,-]=>41
[-,-,4,3,+]=>31
[-,+,4,3,-]=>46
[+,-,4,3,-]=>51
[-,-,4,3,-]=>56
[+,+,4,5,3]=>18
[-,+,4,5,3]=>23
[+,-,4,5,3]=>28
[-,-,4,5,3]=>33
[+,+,5,3,4]=>38
[-,+,5,3,4]=>43
[+,-,5,3,4]=>48
[-,-,5,3,4]=>53
[+,+,5,+,3]=>19
[-,+,5,+,3]=>24
[+,-,5,+,3]=>29
[+,+,5,-,3]=>39
[-,-,5,+,3]=>34
[-,+,5,-,3]=>44
[+,-,5,-,3]=>49
[-,-,5,-,3]=>54
[+,3,2,+,+]=>11
[-,3,2,+,+]=>16
[+,3,2,-,+]=>31
[+,3,2,+,-]=>36
[-,3,2,-,+]=>36
[-,3,2,+,-]=>41
[+,3,2,-,-]=>56
[-,3,2,-,-]=>61
[+,3,2,5,4]=>32
[-,3,2,5,4]=>37
[+,3,4,2,+]=>13
[-,3,4,2,+]=>18
[+,3,4,2,-]=>38
[-,3,4,2,-]=>43
[+,3,4,5,2]=>16
[-,3,4,5,2]=>21
[+,3,5,2,4]=>35
[-,3,5,2,4]=>40
[+,3,5,+,2]=>17
[-,3,5,+,2]=>22
[+,3,5,-,2]=>37
[-,3,5,-,2]=>42
[+,4,2,3,+]=>28
[-,4,2,3,+]=>33
[+,4,2,3,-]=>53
[-,4,2,3,-]=>58
[+,4,2,5,3]=>30
[-,4,2,5,3]=>35
[+,4,+,2,+]=>14
[-,4,+,2,+]=>19
[+,4,-,2,+]=>29
[+,4,+,2,-]=>39
[-,4,-,2,+]=>34
[-,4,+,2,-]=>44
[+,4,-,2,-]=>54
[-,4,-,2,-]=>59
[+,4,+,5,2]=>17
[-,4,+,5,2]=>22
[+,4,-,5,2]=>32
[-,4,-,5,2]=>37
[+,4,5,2,3]=>33
[-,4,5,2,3]=>38
[+,4,5,3,2]=>34
[-,4,5,3,2]=>39
[+,5,2,3,4]=>51
[-,5,2,3,4]=>56
[+,5,2,+,3]=>32
[-,5,2,+,3]=>37
[+,5,2,-,3]=>52
[-,5,2,-,3]=>57
[+,5,+,2,4]=>37
[-,5,+,2,4]=>42
[+,5,-,2,4]=>52
[-,5,-,2,4]=>57
[+,5,+,+,2]=>19
[-,5,+,+,2]=>24
[+,5,-,+,2]=>34
[+,5,+,-,2]=>39
[-,5,-,+,2]=>39
[-,5,+,-,2]=>44
[+,5,-,-,2]=>54
[-,5,-,-,2]=>59
[+,5,4,2,3]=>34
[-,5,4,2,3]=>39
[+,5,4,3,2]=>35
[-,5,4,3,2]=>40
[2,1,+,+,+]=>6
[2,1,-,+,+]=>21
[2,1,+,-,+]=>26
[2,1,+,+,-]=>31
[2,1,-,-,+]=>41
[2,1,-,+,-]=>46
[2,1,+,-,-]=>51
[2,1,-,-,-]=>66
[2,1,+,5,4]=>27
[2,1,-,5,4]=>42
[2,1,4,3,+]=>22
[2,1,4,3,-]=>47
[2,1,4,5,3]=>24
[2,1,5,3,4]=>44
[2,1,5,+,3]=>25
[2,1,5,-,3]=>45
[2,3,1,+,+]=>8
[2,3,1,-,+]=>28
[2,3,1,+,-]=>33
[2,3,1,-,-]=>53
[2,3,1,5,4]=>29
[2,3,4,1,+]=>11
[2,3,4,1,-]=>36
[2,3,4,5,1]=>15
[2,3,5,1,4]=>33
[2,3,5,+,1]=>16
[2,3,5,-,1]=>36
[2,4,1,3,+]=>25
[2,4,1,3,-]=>50
[2,4,1,5,3]=>27
[2,4,+,1,+]=>12
[2,4,-,1,+]=>27
[2,4,+,1,-]=>37
[2,4,-,1,-]=>52
[2,4,+,5,1]=>16
[2,4,-,5,1]=>31
[2,4,5,1,3]=>31
[2,4,5,3,1]=>33
[2,5,1,3,4]=>48
[2,5,1,+,3]=>29
[2,5,1,-,3]=>49
[2,5,+,1,4]=>35
[2,5,-,1,4]=>50
[2,5,+,+,1]=>18
[2,5,-,+,1]=>33
[2,5,+,-,1]=>38
[2,5,-,-,1]=>53
[2,5,4,1,3]=>32
[2,5,4,3,1]=>34
[3,1,2,+,+]=>18
[3,1,2,-,+]=>38
[3,1,2,+,-]=>43
[3,1,2,-,-]=>63
[3,1,2,5,4]=>39
[3,1,4,2,+]=>20
[3,1,4,2,-]=>45
[3,1,4,5,2]=>23
[3,1,5,2,4]=>42
[3,1,5,+,2]=>24
[3,1,5,-,2]=>44
[3,+,1,+,+]=>9
[3,-,1,+,+]=>19
[3,+,1,-,+]=>29
[3,+,1,+,-]=>34
[3,-,1,-,+]=>39
[3,-,1,+,-]=>44
[3,+,1,-,-]=>54
[3,-,1,-,-]=>64
[3,+,1,5,4]=>30
[3,-,1,5,4]=>40
[3,+,4,1,+]=>12
[3,-,4,1,+]=>22
[3,+,4,1,-]=>37
[3,-,4,1,-]=>47
[3,+,4,5,1]=>16
[3,-,4,5,1]=>26
[3,+,5,1,4]=>34
[3,-,5,1,4]=>44
[3,+,5,+,1]=>17
[3,-,5,+,1]=>27
[3,+,5,-,1]=>37
[3,-,5,-,1]=>47
[3,4,1,2,+]=>23
[3,4,1,2,-]=>48
[3,4,1,5,2]=>26
[3,4,2,1,+]=>24
[3,4,2,1,-]=>49
[3,4,2,5,1]=>28
[3,4,5,1,2]=>30
[3,4,5,2,1]=>31
[3,5,1,2,4]=>46
[3,5,1,+,2]=>28
[3,5,1,-,2]=>48
[3,5,2,1,4]=>47
[3,5,2,+,1]=>30
[3,5,2,-,1]=>50
[3,5,4,1,2]=>31
[3,5,4,2,1]=>32
[4,1,2,3,+]=>36
[4,1,2,3,-]=>61
[4,1,2,5,3]=>38
[4,1,+,2,+]=>22
[4,1,-,2,+]=>37
[4,1,+,2,-]=>47
[4,1,-,2,-]=>62
[4,1,+,5,2]=>25
[4,1,-,5,2]=>40
[4,1,5,2,3]=>41
[4,1,5,3,2]=>42
[4,+,1,3,+]=>27
[4,-,1,3,+]=>37
[4,+,1,3,-]=>52
[4,-,1,3,-]=>62
[4,+,1,5,3]=>29
[4,-,1,5,3]=>39
[4,+,+,1,+]=>14
[4,-,+,1,+]=>24
[4,+,-,1,+]=>29
[4,+,+,1,-]=>39
[4,-,-,1,+]=>39
[4,-,+,1,-]=>49
[4,+,-,1,-]=>54
[4,-,-,1,-]=>64
[4,+,+,5,1]=>18
[4,-,+,5,1]=>28
[4,+,-,5,1]=>33
[4,-,-,5,1]=>43
[4,+,5,1,3]=>33
[4,-,5,1,3]=>43
[4,+,5,3,1]=>35
[4,-,5,3,1]=>45
[4,3,1,2,+]=>24
[4,3,1,2,-]=>49
[4,3,1,5,2]=>27
[4,3,2,1,+]=>25
[4,3,2,1,-]=>50
[4,3,2,5,1]=>29
[4,3,5,1,2]=>31
[4,3,5,2,1]=>32
[4,5,1,2,3]=>45
[4,5,1,3,2]=>46
[4,5,2,1,3]=>46
[4,5,2,3,1]=>48
[4,5,+,1,2]=>33
[4,5,-,1,2]=>48
[4,5,+,2,1]=>34
[4,5,-,2,1]=>49
[5,1,2,3,4]=>60
[5,1,2,+,3]=>41
[5,1,2,-,3]=>61
[5,1,+,2,4]=>46
[5,1,-,2,4]=>61
[5,1,+,+,2]=>28
[5,1,-,+,2]=>43
[5,1,+,-,2]=>48
[5,1,-,-,2]=>63
[5,1,4,2,3]=>43
[5,1,4,3,2]=>44
[5,+,1,3,4]=>51
[5,-,1,3,4]=>61
[5,+,1,+,3]=>32
[5,-,1,+,3]=>42
[5,+,1,-,3]=>52
[5,-,1,-,3]=>62
[5,+,+,1,4]=>38
[5,-,+,1,4]=>48
[5,+,-,1,4]=>53
[5,-,-,1,4]=>63
[5,+,+,+,1]=>21
[5,-,+,+,1]=>31
[5,+,-,+,1]=>36
[5,+,+,-,1]=>41
[5,-,-,+,1]=>46
[5,-,+,-,1]=>51
[5,+,-,-,1]=>56
[5,-,-,-,1]=>66
[5,+,4,1,3]=>35
[5,-,4,1,3]=>45
[5,+,4,3,1]=>37
[5,-,4,3,1]=>47
[5,3,1,2,4]=>48
[5,3,1,+,2]=>30
[5,3,1,-,2]=>50
[5,3,2,1,4]=>49
[5,3,2,+,1]=>32
[5,3,2,-,1]=>52
[5,3,4,1,2]=>33
[5,3,4,2,1]=>34
[5,4,1,2,3]=>46
[5,4,1,3,2]=>47
[5,4,2,1,3]=>47
[5,4,2,3,1]=>49
[5,4,+,1,2]=>34
[5,4,-,1,2]=>49
[5,4,+,2,1]=>35
[5,4,-,2,1]=>50
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Description
The sum of all indices from every element of the 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
k=len(tau[0])
for i in range(0,len(tau)):
for j in range(0,k):
sum = sum + tau[i][j]
return sum
Created
May 14, 2020 at 20:41 by Danny Luecke
Updated
May 14, 2020 at 20:41 by Danny Luecke
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