Identifier
Values
=>
[1,2]=>4
[1,-2]=>3
[-1,2]=>3
[-1,-2]=>0
[2,1]=>3
[2,-1]=>0
[-2,1]=>0
[-2,-1]=>3
[1,2,3]=>9
[1,2,-3]=>8
[1,-2,3]=>8
[1,-2,-3]=>5
[-1,2,3]=>8
[-1,2,-3]=>5
[-1,-2,3]=>5
[-1,-2,-3]=>0
[1,3,2]=>8
[1,3,-2]=>5
[1,-3,2]=>5
[1,-3,-2]=>8
[-1,3,2]=>7
[-1,3,-2]=>0
[-1,-3,2]=>0
[-1,-3,-2]=>7
[2,1,3]=>8
[2,1,-3]=>7
[2,-1,3]=>5
[2,-1,-3]=>0
[-2,1,3]=>5
[-2,1,-3]=>0
[-2,-1,3]=>8
[-2,-1,-3]=>7
[2,3,1]=>6
[2,3,-1]=>0
[2,-3,1]=>0
[2,-3,-1]=>6
[-2,3,1]=>0
[-2,3,-1]=>6
[-2,-3,1]=>6
[-2,-3,-1]=>0
[3,1,2]=>6
[3,1,-2]=>0
[3,-1,2]=>0
[3,-1,-2]=>6
[-3,1,2]=>0
[-3,1,-2]=>6
[-3,-1,2]=>6
[-3,-1,-2]=>0
[3,2,1]=>8
[3,2,-1]=>5
[3,-2,1]=>7
[3,-2,-1]=>0
[-3,2,1]=>5
[-3,2,-1]=>8
[-3,-2,1]=>0
[-3,-2,-1]=>7
[1,2,3,4]=>16
[1,2,3,-4]=>15
[1,2,-3,4]=>15
[1,2,-3,-4]=>12
[1,-2,3,4]=>15
[1,-2,3,-4]=>12
[1,-2,-3,4]=>12
[1,-2,-3,-4]=>7
[-1,2,3,4]=>15
[-1,2,3,-4]=>12
[-1,2,-3,4]=>12
[-1,2,-3,-4]=>7
[-1,-2,3,4]=>12
[-1,-2,3,-4]=>7
[-1,-2,-3,4]=>7
[-1,-2,-3,-4]=>0
[1,2,4,3]=>15
[1,2,4,-3]=>12
[1,2,-4,3]=>12
[1,2,-4,-3]=>15
[1,-2,4,3]=>14
[1,-2,4,-3]=>7
[1,-2,-4,3]=>7
[1,-2,-4,-3]=>14
[-1,2,4,3]=>14
[-1,2,4,-3]=>7
[-1,2,-4,3]=>7
[-1,2,-4,-3]=>14
[-1,-2,4,3]=>11
[-1,-2,4,-3]=>0
[-1,-2,-4,3]=>0
[-1,-2,-4,-3]=>11
[1,3,2,4]=>15
[1,3,2,-4]=>14
[1,3,-2,4]=>12
[1,3,-2,-4]=>7
[1,-3,2,4]=>12
[1,-3,2,-4]=>7
[1,-3,-2,4]=>15
[1,-3,-2,-4]=>14
[-1,3,2,4]=>14
[-1,3,2,-4]=>11
[-1,3,-2,4]=>7
[-1,3,-2,-4]=>0
[-1,-3,2,4]=>7
[-1,-3,2,-4]=>0
[-1,-3,-2,4]=>14
[-1,-3,-2,-4]=>11
[1,3,4,2]=>13
[1,3,4,-2]=>7
[1,3,-4,2]=>7
[1,3,-4,-2]=>13
[1,-3,4,2]=>7
[1,-3,4,-2]=>13
[1,-3,-4,2]=>13
[1,-3,-4,-2]=>7
[-1,3,4,2]=>12
[-1,3,4,-2]=>0
[-1,3,-4,2]=>0
[-1,3,-4,-2]=>12
[-1,-3,4,2]=>0
[-1,-3,4,-2]=>12
[-1,-3,-4,2]=>12
[-1,-3,-4,-2]=>0
[1,4,2,3]=>13
[1,4,2,-3]=>7
[1,4,-2,3]=>7
[1,4,-2,-3]=>13
[1,-4,2,3]=>7
[1,-4,2,-3]=>13
[1,-4,-2,3]=>13
[1,-4,-2,-3]=>7
[-1,4,2,3]=>12
[-1,4,2,-3]=>0
[-1,4,-2,3]=>0
[-1,4,-2,-3]=>12
[-1,-4,2,3]=>0
[-1,-4,2,-3]=>12
[-1,-4,-2,3]=>12
[-1,-4,-2,-3]=>0
[1,4,3,2]=>15
[1,4,3,-2]=>12
[1,4,-3,2]=>14
[1,4,-3,-2]=>7
[1,-4,3,2]=>12
[1,-4,3,-2]=>15
[1,-4,-3,2]=>7
[1,-4,-3,-2]=>14
[-1,4,3,2]=>14
[-1,4,3,-2]=>7
[-1,4,-3,2]=>11
[-1,4,-3,-2]=>0
[-1,-4,3,2]=>7
[-1,-4,3,-2]=>14
[-1,-4,-3,2]=>0
[-1,-4,-3,-2]=>11
[2,1,3,4]=>15
[2,1,3,-4]=>14
[2,1,-3,4]=>14
[2,1,-3,-4]=>11
[2,-1,3,4]=>12
[2,-1,3,-4]=>7
[2,-1,-3,4]=>7
[2,-1,-3,-4]=>0
[-2,1,3,4]=>12
[-2,1,3,-4]=>7
[-2,1,-3,4]=>7
[-2,1,-3,-4]=>0
[-2,-1,3,4]=>15
[-2,-1,3,-4]=>14
[-2,-1,-3,4]=>14
[-2,-1,-3,-4]=>11
[2,1,4,3]=>14
[2,1,4,-3]=>11
[2,1,-4,3]=>11
[2,1,-4,-3]=>14
[2,-1,4,3]=>11
[2,-1,4,-3]=>0
[2,-1,-4,3]=>0
[2,-1,-4,-3]=>11
[-2,1,4,3]=>11
[-2,1,4,-3]=>0
[-2,1,-4,3]=>0
[-2,1,-4,-3]=>11
[-2,-1,4,3]=>14
[-2,-1,4,-3]=>11
[-2,-1,-4,3]=>11
[-2,-1,-4,-3]=>14
[2,3,1,4]=>13
[2,3,1,-4]=>12
[2,3,-1,4]=>7
[2,3,-1,-4]=>0
[2,-3,1,4]=>7
[2,-3,1,-4]=>0
[2,-3,-1,4]=>13
[2,-3,-1,-4]=>12
[-2,3,1,4]=>7
[-2,3,1,-4]=>0
[-2,3,-1,4]=>13
[-2,3,-1,-4]=>12
[-2,-3,1,4]=>13
[-2,-3,1,-4]=>12
[-2,-3,-1,4]=>7
[-2,-3,-1,-4]=>0
[2,3,4,1]=>10
[2,3,4,-1]=>0
[2,3,-4,1]=>0
[2,3,-4,-1]=>10
[2,-3,4,1]=>0
[2,-3,4,-1]=>10
[2,-3,-4,1]=>10
[2,-3,-4,-1]=>0
[-2,3,4,1]=>0
[-2,3,4,-1]=>10
[-2,3,-4,1]=>10
[-2,3,-4,-1]=>0
[-2,-3,4,1]=>10
[-2,-3,4,-1]=>0
[-2,-3,-4,1]=>0
[-2,-3,-4,-1]=>10
[2,4,1,3]=>10
[2,4,1,-3]=>0
[2,4,-1,3]=>0
[2,4,-1,-3]=>10
[2,-4,1,3]=>0
[2,-4,1,-3]=>10
[2,-4,-1,3]=>10
[2,-4,-1,-3]=>0
[-2,4,1,3]=>0
[-2,4,1,-3]=>10
[-2,4,-1,3]=>10
[-2,4,-1,-3]=>0
[-2,-4,1,3]=>10
[-2,-4,1,-3]=>0
[-2,-4,-1,3]=>0
[-2,-4,-1,-3]=>10
[2,4,3,1]=>13
[2,4,3,-1]=>7
[2,4,-3,1]=>12
[2,4,-3,-1]=>0
[2,-4,3,1]=>7
[2,-4,3,-1]=>13
[2,-4,-3,1]=>0
[2,-4,-3,-1]=>12
[-2,4,3,1]=>7
[-2,4,3,-1]=>13
[-2,4,-3,1]=>0
[-2,4,-3,-1]=>12
[-2,-4,3,1]=>13
[-2,-4,3,-1]=>7
[-2,-4,-3,1]=>12
[-2,-4,-3,-1]=>0
[3,1,2,4]=>13
[3,1,2,-4]=>12
[3,1,-2,4]=>7
[3,1,-2,-4]=>0
[3,-1,2,4]=>7
[3,-1,2,-4]=>0
[3,-1,-2,4]=>13
[3,-1,-2,-4]=>12
[-3,1,2,4]=>7
[-3,1,2,-4]=>0
[-3,1,-2,4]=>13
[-3,1,-2,-4]=>12
[-3,-1,2,4]=>13
[-3,-1,2,-4]=>12
[-3,-1,-2,4]=>7
[-3,-1,-2,-4]=>0
[3,1,4,2]=>10
[3,1,4,-2]=>0
[3,1,-4,2]=>0
[3,1,-4,-2]=>10
[3,-1,4,2]=>0
[3,-1,4,-2]=>10
[3,-1,-4,2]=>10
[3,-1,-4,-2]=>0
[-3,1,4,2]=>0
[-3,1,4,-2]=>10
[-3,1,-4,2]=>10
[-3,1,-4,-2]=>0
[-3,-1,4,2]=>10
[-3,-1,4,-2]=>0
[-3,-1,-4,2]=>0
[-3,-1,-4,-2]=>10
[3,2,1,4]=>15
[3,2,1,-4]=>14
[3,2,-1,4]=>12
[3,2,-1,-4]=>7
[3,-2,1,4]=>14
[3,-2,1,-4]=>11
[3,-2,-1,4]=>7
[3,-2,-1,-4]=>0
[-3,2,1,4]=>12
[-3,2,1,-4]=>7
[-3,2,-1,4]=>15
[-3,2,-1,-4]=>14
[-3,-2,1,4]=>7
[-3,-2,1,-4]=>0
[-3,-2,-1,4]=>14
[-3,-2,-1,-4]=>11
[3,2,4,1]=>13
[3,2,4,-1]=>7
[3,2,-4,1]=>7
[3,2,-4,-1]=>13
[3,-2,4,1]=>12
[3,-2,4,-1]=>0
[3,-2,-4,1]=>0
[3,-2,-4,-1]=>12
[-3,2,4,1]=>7
[-3,2,4,-1]=>13
[-3,2,-4,1]=>13
[-3,2,-4,-1]=>7
[-3,-2,4,1]=>0
[-3,-2,4,-1]=>12
[-3,-2,-4,1]=>12
[-3,-2,-4,-1]=>0
[3,4,1,2]=>14
[3,4,1,-2]=>11
[3,4,-1,2]=>11
[3,4,-1,-2]=>0
[3,-4,1,2]=>11
[3,-4,1,-2]=>14
[3,-4,-1,2]=>0
[3,-4,-1,-2]=>11
[-3,4,1,2]=>11
[-3,4,1,-2]=>0
[-3,4,-1,2]=>14
[-3,4,-1,-2]=>11
[-3,-4,1,2]=>0
[-3,-4,1,-2]=>11
[-3,-4,-1,2]=>11
[-3,-4,-1,-2]=>14
[3,4,2,1]=>10
[3,4,2,-1]=>0
[3,4,-2,1]=>0
[3,4,-2,-1]=>10
[3,-4,2,1]=>0
[3,-4,2,-1]=>10
[3,-4,-2,1]=>10
[3,-4,-2,-1]=>0
[-3,4,2,1]=>0
[-3,4,2,-1]=>10
[-3,4,-2,1]=>10
[-3,4,-2,-1]=>0
[-3,-4,2,1]=>10
[-3,-4,2,-1]=>0
[-3,-4,-2,1]=>0
[-3,-4,-2,-1]=>10
[4,1,2,3]=>10
[4,1,2,-3]=>0
[4,1,-2,3]=>0
[4,1,-2,-3]=>10
[4,-1,2,3]=>0
[4,-1,2,-3]=>10
[4,-1,-2,3]=>10
[4,-1,-2,-3]=>0
[-4,1,2,3]=>0
[-4,1,2,-3]=>10
[-4,1,-2,3]=>10
[-4,1,-2,-3]=>0
[-4,-1,2,3]=>10
[-4,-1,2,-3]=>0
[-4,-1,-2,3]=>0
[-4,-1,-2,-3]=>10
[4,1,3,2]=>13
[4,1,3,-2]=>7
[4,1,-3,2]=>12
[4,1,-3,-2]=>0
[4,-1,3,2]=>7
[4,-1,3,-2]=>13
[4,-1,-3,2]=>0
[4,-1,-3,-2]=>12
[-4,1,3,2]=>7
[-4,1,3,-2]=>13
[-4,1,-3,2]=>0
[-4,1,-3,-2]=>12
[-4,-1,3,2]=>13
[-4,-1,3,-2]=>7
[-4,-1,-3,2]=>12
[-4,-1,-3,-2]=>0
[4,2,1,3]=>13
[4,2,1,-3]=>7
[4,2,-1,3]=>7
[4,2,-1,-3]=>13
[4,-2,1,3]=>12
[4,-2,1,-3]=>0
[4,-2,-1,3]=>0
[4,-2,-1,-3]=>12
[-4,2,1,3]=>7
[-4,2,1,-3]=>13
[-4,2,-1,3]=>13
[-4,2,-1,-3]=>7
[-4,-2,1,3]=>0
[-4,-2,1,-3]=>12
[-4,-2,-1,3]=>12
[-4,-2,-1,-3]=>0
[4,2,3,1]=>15
[4,2,3,-1]=>12
[4,2,-3,1]=>14
[4,2,-3,-1]=>7
[4,-2,3,1]=>14
[4,-2,3,-1]=>7
[4,-2,-3,1]=>11
[4,-2,-3,-1]=>0
[-4,2,3,1]=>12
[-4,2,3,-1]=>15
[-4,2,-3,1]=>7
[-4,2,-3,-1]=>14
[-4,-2,3,1]=>7
[-4,-2,3,-1]=>14
[-4,-2,-3,1]=>0
[-4,-2,-3,-1]=>11
[4,3,1,2]=>10
[4,3,1,-2]=>0
[4,3,-1,2]=>0
[4,3,-1,-2]=>10
[4,-3,1,2]=>0
[4,-3,1,-2]=>10
[4,-3,-1,2]=>10
[4,-3,-1,-2]=>0
[-4,3,1,2]=>0
[-4,3,1,-2]=>10
[-4,3,-1,2]=>10
[-4,3,-1,-2]=>0
[-4,-3,1,2]=>10
[-4,-3,1,-2]=>0
[-4,-3,-1,2]=>0
[-4,-3,-1,-2]=>10
[4,3,2,1]=>14
[4,3,2,-1]=>11
[4,3,-2,1]=>11
[4,3,-2,-1]=>0
[4,-3,2,1]=>11
[4,-3,2,-1]=>0
[4,-3,-2,1]=>14
[4,-3,-2,-1]=>11
[-4,3,2,1]=>11
[-4,3,2,-1]=>14
[-4,3,-2,1]=>0
[-4,3,-2,-1]=>11
[-4,-3,2,1]=>0
[-4,-3,2,-1]=>11
[-4,-3,-2,1]=>11
[-4,-3,-2,-1]=>14
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Description
The number of covering elements of a signed permutation in absolute order.
Code
def statistic(pi):
return len(WeylGroup(["B", len(pi)]).from_reduced_word(pi.reduced_word()).absolute_covers())
Created
Nov 27, 2022 at 21:47 by Martin Rubey
Updated
Jan 08, 2023 at 15:05 by Martin Rubey
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