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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001858
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The number of covering elements of a signed permutation in absolute order.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(pi):
return len(WeylGroup(["B", len(pi)]).from_reduced_word(pi.reduced_word()).absolute_covers())
-----------------------------------------------------------------------------
Statistic 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
-----------------------------------------------------------------------------
Created: Nov 27, 2022 at 21:47 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jan 08, 2023 at 15:05 by Martin Rubey