Identifier
Values
=>
[1]=>0
[-1]=>1
[1,2]=>0
[1,-2]=>1
[-1,2]=>1
[-1,-2]=>2
[2,1]=>2
[2,-1]=>3
[-2,1]=>3
[-2,-1]=>4
[1,2,3]=>0
[1,2,-3]=>1
[1,-2,3]=>1
[1,-2,-3]=>2
[-1,2,3]=>1
[-1,2,-3]=>2
[-1,-2,3]=>2
[-1,-2,-3]=>3
[1,3,2]=>4
[1,3,-2]=>5
[1,-3,2]=>5
[1,-3,-2]=>6
[-1,3,2]=>5
[-1,3,-2]=>6
[-1,-3,2]=>6
[-1,-3,-2]=>7
[2,1,3]=>2
[2,1,-3]=>3
[2,-1,3]=>3
[2,-1,-3]=>4
[-2,1,3]=>3
[-2,1,-3]=>4
[-2,-1,3]=>4
[-2,-1,-3]=>5
[2,3,1]=>6
[2,3,-1]=>7
[2,-3,1]=>7
[2,-3,-1]=>8
[-2,3,1]=>7
[-2,3,-1]=>8
[-2,-3,1]=>8
[-2,-3,-1]=>9
[3,1,2]=>2
[3,1,-2]=>3
[3,-1,2]=>3
[3,-1,-2]=>4
[-3,1,2]=>3
[-3,1,-2]=>4
[-3,-1,2]=>4
[-3,-1,-2]=>5
[3,2,1]=>4
[3,2,-1]=>5
[3,-2,1]=>5
[3,-2,-1]=>6
[-3,2,1]=>5
[-3,2,-1]=>6
[-3,-2,1]=>6
[-3,-2,-1]=>7
[1,2,3,4]=>0
[1,2,3,-4]=>1
[1,2,-3,4]=>1
[1,2,-3,-4]=>2
[1,-2,3,4]=>1
[1,-2,3,-4]=>2
[1,-2,-3,4]=>2
[1,-2,-3,-4]=>3
[-1,2,3,4]=>1
[-1,2,3,-4]=>2
[-1,2,-3,4]=>2
[-1,2,-3,-4]=>3
[-1,-2,3,4]=>2
[-1,-2,3,-4]=>3
[-1,-2,-3,4]=>3
[-1,-2,-3,-4]=>4
[1,2,4,3]=>6
[1,2,4,-3]=>7
[1,2,-4,3]=>7
[1,2,-4,-3]=>8
[1,-2,4,3]=>7
[1,-2,4,-3]=>8
[1,-2,-4,3]=>8
[1,-2,-4,-3]=>9
[-1,2,4,3]=>7
[-1,2,4,-3]=>8
[-1,2,-4,3]=>8
[-1,2,-4,-3]=>9
[-1,-2,4,3]=>8
[-1,-2,4,-3]=>9
[-1,-2,-4,3]=>9
[-1,-2,-4,-3]=>10
[1,3,2,4]=>4
[1,3,2,-4]=>5
[1,3,-2,4]=>5
[1,3,-2,-4]=>6
[1,-3,2,4]=>5
[1,-3,2,-4]=>6
[1,-3,-2,4]=>6
[1,-3,-2,-4]=>7
[-1,3,2,4]=>5
[-1,3,2,-4]=>6
[-1,3,-2,4]=>6
[-1,3,-2,-4]=>7
[-1,-3,2,4]=>6
[-1,-3,2,-4]=>7
[-1,-3,-2,4]=>7
[-1,-3,-2,-4]=>8
[1,3,4,2]=>10
[1,3,4,-2]=>11
[1,3,-4,2]=>11
[1,3,-4,-2]=>12
[1,-3,4,2]=>11
[1,-3,4,-2]=>12
[1,-3,-4,2]=>12
[1,-3,-4,-2]=>13
[-1,3,4,2]=>11
[-1,3,4,-2]=>12
[-1,3,-4,2]=>12
[-1,3,-4,-2]=>13
[-1,-3,4,2]=>12
[-1,-3,4,-2]=>13
[-1,-3,-4,2]=>13
[-1,-3,-4,-2]=>14
[1,4,2,3]=>4
[1,4,2,-3]=>5
[1,4,-2,3]=>5
[1,4,-2,-3]=>6
[1,-4,2,3]=>5
[1,-4,2,-3]=>6
[1,-4,-2,3]=>6
[1,-4,-2,-3]=>7
[-1,4,2,3]=>5
[-1,4,2,-3]=>6
[-1,4,-2,3]=>6
[-1,4,-2,-3]=>7
[-1,-4,2,3]=>6
[-1,-4,2,-3]=>7
[-1,-4,-2,3]=>7
[-1,-4,-2,-3]=>8
[1,4,3,2]=>6
[1,4,3,-2]=>7
[1,4,-3,2]=>7
[1,4,-3,-2]=>8
[1,-4,3,2]=>7
[1,-4,3,-2]=>8
[1,-4,-3,2]=>8
[1,-4,-3,-2]=>9
[-1,4,3,2]=>7
[-1,4,3,-2]=>8
[-1,4,-3,2]=>8
[-1,4,-3,-2]=>9
[-1,-4,3,2]=>8
[-1,-4,3,-2]=>9
[-1,-4,-3,2]=>9
[-1,-4,-3,-2]=>10
[2,1,3,4]=>2
[2,1,3,-4]=>3
[2,1,-3,4]=>3
[2,1,-3,-4]=>4
[2,-1,3,4]=>3
[2,-1,3,-4]=>4
[2,-1,-3,4]=>4
[2,-1,-3,-4]=>5
[-2,1,3,4]=>3
[-2,1,3,-4]=>4
[-2,1,-3,4]=>4
[-2,1,-3,-4]=>5
[-2,-1,3,4]=>4
[-2,-1,3,-4]=>5
[-2,-1,-3,4]=>5
[-2,-1,-3,-4]=>6
[2,1,4,3]=>8
[2,1,4,-3]=>9
[2,1,-4,3]=>9
[2,1,-4,-3]=>10
[2,-1,4,3]=>9
[2,-1,4,-3]=>10
[2,-1,-4,3]=>10
[2,-1,-4,-3]=>11
[-2,1,4,3]=>9
[-2,1,4,-3]=>10
[-2,1,-4,3]=>10
[-2,1,-4,-3]=>11
[-2,-1,4,3]=>10
[-2,-1,4,-3]=>11
[-2,-1,-4,3]=>11
[-2,-1,-4,-3]=>12
[2,3,1,4]=>6
[2,3,1,-4]=>7
[2,3,-1,4]=>7
[2,3,-1,-4]=>8
[2,-3,1,4]=>7
[2,-3,1,-4]=>8
[2,-3,-1,4]=>8
[2,-3,-1,-4]=>9
[-2,3,1,4]=>7
[-2,3,1,-4]=>8
[-2,3,-1,4]=>8
[-2,3,-1,-4]=>9
[-2,-3,1,4]=>8
[-2,-3,1,-4]=>9
[-2,-3,-1,4]=>9
[-2,-3,-1,-4]=>10
[2,3,4,1]=>12
[2,3,4,-1]=>13
[2,3,-4,1]=>13
[2,3,-4,-1]=>14
[2,-3,4,1]=>13
[2,-3,4,-1]=>14
[2,-3,-4,1]=>14
[2,-3,-4,-1]=>15
[-2,3,4,1]=>13
[-2,3,4,-1]=>14
[-2,3,-4,1]=>14
[-2,3,-4,-1]=>15
[-2,-3,4,1]=>14
[-2,-3,4,-1]=>15
[-2,-3,-4,1]=>15
[-2,-3,-4,-1]=>16
[2,4,1,3]=>6
[2,4,1,-3]=>7
[2,4,-1,3]=>7
[2,4,-1,-3]=>8
[2,-4,1,3]=>7
[2,-4,1,-3]=>8
[2,-4,-1,3]=>8
[2,-4,-1,-3]=>9
[-2,4,1,3]=>7
[-2,4,1,-3]=>8
[-2,4,-1,3]=>8
[-2,4,-1,-3]=>9
[-2,-4,1,3]=>8
[-2,-4,1,-3]=>9
[-2,-4,-1,3]=>9
[-2,-4,-1,-3]=>10
[2,4,3,1]=>8
[2,4,3,-1]=>9
[2,4,-3,1]=>9
[2,4,-3,-1]=>10
[2,-4,3,1]=>9
[2,-4,3,-1]=>10
[2,-4,-3,1]=>10
[2,-4,-3,-1]=>11
[-2,4,3,1]=>9
[-2,4,3,-1]=>10
[-2,4,-3,1]=>10
[-2,4,-3,-1]=>11
[-2,-4,3,1]=>10
[-2,-4,3,-1]=>11
[-2,-4,-3,1]=>11
[-2,-4,-3,-1]=>12
[3,1,2,4]=>2
[3,1,2,-4]=>3
[3,1,-2,4]=>3
[3,1,-2,-4]=>4
[3,-1,2,4]=>3
[3,-1,2,-4]=>4
[3,-1,-2,4]=>4
[3,-1,-2,-4]=>5
[-3,1,2,4]=>3
[-3,1,2,-4]=>4
[-3,1,-2,4]=>4
[-3,1,-2,-4]=>5
[-3,-1,2,4]=>4
[-3,-1,2,-4]=>5
[-3,-1,-2,4]=>5
[-3,-1,-2,-4]=>6
[3,1,4,2]=>8
[3,1,4,-2]=>9
[3,1,-4,2]=>9
[3,1,-4,-2]=>10
[3,-1,4,2]=>9
[3,-1,4,-2]=>10
[3,-1,-4,2]=>10
[3,-1,-4,-2]=>11
[-3,1,4,2]=>9
[-3,1,4,-2]=>10
[-3,1,-4,2]=>10
[-3,1,-4,-2]=>11
[-3,-1,4,2]=>10
[-3,-1,4,-2]=>11
[-3,-1,-4,2]=>11
[-3,-1,-4,-2]=>12
[3,2,1,4]=>4
[3,2,1,-4]=>5
[3,2,-1,4]=>5
[3,2,-1,-4]=>6
[3,-2,1,4]=>5
[3,-2,1,-4]=>6
[3,-2,-1,4]=>6
[3,-2,-1,-4]=>7
[-3,2,1,4]=>5
[-3,2,1,-4]=>6
[-3,2,-1,4]=>6
[-3,2,-1,-4]=>7
[-3,-2,1,4]=>6
[-3,-2,1,-4]=>7
[-3,-2,-1,4]=>7
[-3,-2,-1,-4]=>8
[3,2,4,1]=>10
[3,2,4,-1]=>11
[3,2,-4,1]=>11
[3,2,-4,-1]=>12
[3,-2,4,1]=>11
[3,-2,4,-1]=>12
[3,-2,-4,1]=>12
[3,-2,-4,-1]=>13
[-3,2,4,1]=>11
[-3,2,4,-1]=>12
[-3,2,-4,1]=>12
[-3,2,-4,-1]=>13
[-3,-2,4,1]=>12
[-3,-2,4,-1]=>13
[-3,-2,-4,1]=>13
[-3,-2,-4,-1]=>14
[3,4,1,2]=>6
[3,4,1,-2]=>7
[3,4,-1,2]=>7
[3,4,-1,-2]=>8
[3,-4,1,2]=>7
[3,-4,1,-2]=>8
[3,-4,-1,2]=>8
[3,-4,-1,-2]=>9
[-3,4,1,2]=>7
[-3,4,1,-2]=>8
[-3,4,-1,2]=>8
[-3,4,-1,-2]=>9
[-3,-4,1,2]=>8
[-3,-4,1,-2]=>9
[-3,-4,-1,2]=>9
[-3,-4,-1,-2]=>10
[3,4,2,1]=>8
[3,4,2,-1]=>9
[3,4,-2,1]=>9
[3,4,-2,-1]=>10
[3,-4,2,1]=>9
[3,-4,2,-1]=>10
[3,-4,-2,1]=>10
[3,-4,-2,-1]=>11
[-3,4,2,1]=>9
[-3,4,2,-1]=>10
[-3,4,-2,1]=>10
[-3,4,-2,-1]=>11
[-3,-4,2,1]=>10
[-3,-4,2,-1]=>11
[-3,-4,-2,1]=>11
[-3,-4,-2,-1]=>12
[4,1,2,3]=>2
[4,1,2,-3]=>3
[4,1,-2,3]=>3
[4,1,-2,-3]=>4
[4,-1,2,3]=>3
[4,-1,2,-3]=>4
[4,-1,-2,3]=>4
[4,-1,-2,-3]=>5
[-4,1,2,3]=>3
[-4,1,2,-3]=>4
[-4,1,-2,3]=>4
[-4,1,-2,-3]=>5
[-4,-1,2,3]=>4
[-4,-1,2,-3]=>5
[-4,-1,-2,3]=>5
[-4,-1,-2,-3]=>6
[4,1,3,2]=>4
[4,1,3,-2]=>5
[4,1,-3,2]=>5
[4,1,-3,-2]=>6
[4,-1,3,2]=>5
[4,-1,3,-2]=>6
[4,-1,-3,2]=>6
[4,-1,-3,-2]=>7
[-4,1,3,2]=>5
[-4,1,3,-2]=>6
[-4,1,-3,2]=>6
[-4,1,-3,-2]=>7
[-4,-1,3,2]=>6
[-4,-1,3,-2]=>7
[-4,-1,-3,2]=>7
[-4,-1,-3,-2]=>8
[4,2,1,3]=>4
[4,2,1,-3]=>5
[4,2,-1,3]=>5
[4,2,-1,-3]=>6
[4,-2,1,3]=>5
[4,-2,1,-3]=>6
[4,-2,-1,3]=>6
[4,-2,-1,-3]=>7
[-4,2,1,3]=>5
[-4,2,1,-3]=>6
[-4,2,-1,3]=>6
[-4,2,-1,-3]=>7
[-4,-2,1,3]=>6
[-4,-2,1,-3]=>7
[-4,-2,-1,3]=>7
[-4,-2,-1,-3]=>8
[4,2,3,1]=>6
[4,2,3,-1]=>7
[4,2,-3,1]=>7
[4,2,-3,-1]=>8
[4,-2,3,1]=>7
[4,-2,3,-1]=>8
[4,-2,-3,1]=>8
[4,-2,-3,-1]=>9
[-4,2,3,1]=>7
[-4,2,3,-1]=>8
[-4,2,-3,1]=>8
[-4,2,-3,-1]=>9
[-4,-2,3,1]=>8
[-4,-2,3,-1]=>9
[-4,-2,-3,1]=>9
[-4,-2,-3,-1]=>10
[4,3,1,2]=>8
[4,3,1,-2]=>9
[4,3,-1,2]=>9
[4,3,-1,-2]=>10
[4,-3,1,2]=>9
[4,-3,1,-2]=>10
[4,-3,-1,2]=>10
[4,-3,-1,-2]=>11
[-4,3,1,2]=>9
[-4,3,1,-2]=>10
[-4,3,-1,2]=>10
[-4,3,-1,-2]=>11
[-4,-3,1,2]=>10
[-4,-3,1,-2]=>11
[-4,-3,-1,2]=>11
[-4,-3,-1,-2]=>12
[4,3,2,1]=>10
[4,3,2,-1]=>11
[4,3,-2,1]=>11
[4,3,-2,-1]=>12
[4,-3,2,1]=>11
[4,-3,2,-1]=>12
[4,-3,-2,1]=>12
[4,-3,-2,-1]=>13
[-4,3,2,1]=>11
[-4,3,2,-1]=>12
[-4,3,-2,1]=>12
[-4,3,-2,-1]=>13
[-4,-3,2,1]=>12
[-4,-3,2,-1]=>13
[-4,-3,-2,1]=>13
[-4,-3,-2,-1]=>14
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 flag Denert index of a signed permutation.
The flag Denert index of a signed permutation $\sigma$ is:
$$fden(\sigma) = \operatorname{neg}(\sigma) + 2 \cdot den_B(\sigma),$$
where $den_B(\sigma) = den(perm(\sigma))$ is the Denert index of the associated permutation to $\sigma$.
The flag Denert index of a signed permutation $\sigma$ is:
$$fden(\sigma) = \operatorname{neg}(\sigma) + 2 \cdot den_B(\sigma),$$
where $den_B(\sigma) = den(perm(\sigma))$ is the Denert index of the associated permutation to $\sigma$.
References
[1] Fire, M. Statistics on Wreath Products arXiv:math/0409421
Code
def statistic(pi):
n = pi.parent().rank()
A = sum(1 for l,k in Subsets(range(n),2) if abs(pi[k]) < abs(pi[l]) <= k+1 )
B = sum(1 for l,k in Subsets(range(n),2) if abs(pi[l]) <= k+1 < abs(pi[k]) )
C = sum(1 for l,k in Subsets(range(n),2) if k+1 < abs(pi[k]) < abs(pi[l]) )
den_B = A+B+C
neg = len([i for i in pi if i < 0])
return neg + 2 * den_B
Created
Jul 20, 2022 at 08:55 by Dennis Jahn
Updated
Jul 20, 2022 at 08:55 by Dennis Jahn
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!