*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001854
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The size of the left Kazhdan-Lusztig cell,
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(pi):
return len(pi.kazhdan_lusztig_cell("left"))
-----------------------------------------------------------------------------
Statistic values:
[1,2] => 1
[1,-2] => 3
[-1,2] => 3
[-1,-2] => 1
[2,1] => 3
[2,-1] => 3
[-2,1] => 3
[-2,-1] => 3
[1,2,3] => 1
[1,2,-3] => 4
[1,-2,3] => 5
[1,-2,-3] => 5
[-1,2,3] => 5
[-1,2,-3] => 5
[-1,-2,3] => 4
[-1,-2,-3] => 1
[1,3,2] => 5
[1,3,-2] => 5
[1,-3,2] => 4
[1,-3,-2] => 4
[-1,3,2] => 4
[-1,3,-2] => 4
[-1,-3,2] => 5
[-1,-3,-2] => 5
[2,1,3] => 5
[2,1,-3] => 3
[2,-1,3] => 5
[2,-1,-3] => 5
[-2,1,3] => 5
[-2,1,-3] => 5
[-2,-1,3] => 3
[-2,-1,-3] => 5
[2,3,1] => 5
[2,3,-1] => 5
[2,-3,1] => 3
[2,-3,-1] => 3
[-2,3,1] => 3
[-2,3,-1] => 3
[-2,-3,1] => 5
[-2,-3,-1] => 5
[3,1,2] => 5
[3,1,-2] => 3
[3,-1,2] => 3
[3,-1,-2] => 4
[-3,1,2] => 4
[-3,1,-2] => 3
[-3,-1,2] => 3
[-3,-1,-2] => 5
[3,2,1] => 3
[3,2,-1] => 3
[3,-2,1] => 3
[3,-2,-1] => 3
[-3,2,1] => 3
[-3,2,-1] => 3
[-3,-2,1] => 3
[-3,-2,-1] => 3
[1,2,3,4] => 1
[1,2,3,-4] => 5
[1,2,-3,4] => 7
[1,2,-3,-4] => 9
[1,-2,3,4] => 7
[1,-2,3,-4] => 9
[1,-2,-3,4] => 9
[1,-2,-3,-4] => 7
[-1,2,3,4] => 7
[-1,2,3,-4] => 9
[-1,2,-3,4] => 9
[-1,2,-3,-4] => 7
[-1,-2,3,4] => 9
[-1,-2,3,-4] => 7
[-1,-2,-3,4] => 5
[-1,-2,-3,-4] => 1
[1,2,4,3] => 7
[1,2,4,-3] => 7
[1,2,-4,3] => 5
[1,2,-4,-3] => 5
[1,-2,4,3] => 9
[1,-2,4,-3] => 9
[1,-2,-4,3] => 9
[1,-2,-4,-3] => 9
[-1,2,4,3] => 9
[-1,2,4,-3] => 9
[-1,2,-4,3] => 9
[-1,2,-4,-3] => 9
[-1,-2,4,3] => 5
[-1,-2,4,-3] => 5
[-1,-2,-4,3] => 7
[-1,-2,-4,-3] => 7
[1,3,2,4] => 7
[1,3,2,-4] => 10
[1,3,-2,4] => 7
[1,3,-2,-4] => 9
[1,-3,2,4] => 7
[1,-3,2,-4] => 9
[1,-3,-2,4] => 8
[1,-3,-2,-4] => 9
[-1,3,2,4] => 9
[-1,3,2,-4] => 8
[-1,3,-2,4] => 9
[-1,3,-2,-4] => 7
[-1,-3,2,4] => 9
[-1,-3,2,-4] => 7
[-1,-3,-2,4] => 10
[-1,-3,-2,-4] => 7
[1,3,4,2] => 7
[1,3,4,-2] => 7
[1,3,-4,2] => 10
[1,3,-4,-2] => 10
[1,-3,4,2] => 8
[1,-3,4,-2] => 8
[1,-3,-4,2] => 9
[1,-3,-4,-2] => 9
[-1,3,4,2] => 9
[-1,3,4,-2] => 9
[-1,3,-4,2] => 8
[-1,3,-4,-2] => 8
[-1,-3,4,2] => 10
[-1,-3,4,-2] => 10
[-1,-3,-4,2] => 7
[-1,-3,-4,-2] => 7
[1,4,2,3] => 7
[1,4,2,-3] => 10
[1,4,-2,3] => 8
[1,4,-2,-3] => 9
[1,-4,2,3] => 5
[1,-4,2,-3] => 10
[1,-4,-2,3] => 8
[1,-4,-2,-3] => 9
[-1,4,2,3] => 9
[-1,4,2,-3] => 8
[-1,4,-2,3] => 10
[-1,4,-2,-3] => 5
[-1,-4,2,3] => 9
[-1,-4,2,-3] => 8
[-1,-4,-2,3] => 10
[-1,-4,-2,-3] => 7
[1,4,3,2] => 8
[1,4,3,-2] => 8
[1,4,-3,2] => 10
[1,4,-3,-2] => 10
[1,-4,3,2] => 8
[1,-4,3,-2] => 8
[1,-4,-3,2] => 10
[1,-4,-3,-2] => 10
[-1,4,3,2] => 10
[-1,4,3,-2] => 10
[-1,4,-3,2] => 8
[-1,4,-3,-2] => 8
[-1,-4,3,2] => 10
[-1,-4,3,-2] => 10
[-1,-4,-3,2] => 8
[-1,-4,-3,-2] => 8
[2,1,3,4] => 7
[2,1,3,-4] => 10
[2,1,-3,4] => 8
[2,1,-3,-4] => 8
[2,-1,3,4] => 7
[2,-1,3,-4] => 9
[2,-1,-3,4] => 9
[2,-1,-3,-4] => 7
[-2,1,3,4] => 7
[-2,1,3,-4] => 9
[-2,1,-3,4] => 9
[-2,1,-3,-4] => 7
[-2,-1,3,4] => 8
[-2,-1,3,-4] => 8
[-2,-1,-3,4] => 10
[-2,-1,-3,-4] => 7
[2,1,4,3] => 8
[2,1,4,-3] => 8
[2,1,-4,3] => 10
[2,1,-4,-3] => 10
[2,-1,4,3] => 9
[2,-1,4,-3] => 9
[2,-1,-4,3] => 9
[2,-1,-4,-3] => 9
[-2,1,4,3] => 9
[-2,1,4,-3] => 9
[-2,1,-4,3] => 9
[-2,1,-4,-3] => 9
[-2,-1,4,3] => 10
[-2,-1,4,-3] => 10
[-2,-1,-4,3] => 8
[-2,-1,-4,-3] => 8
[2,3,1,4] => 7
[2,3,1,-4] => 10
[2,3,-1,4] => 7
[2,3,-1,-4] => 9
[2,-3,1,4] => 8
[2,-3,1,-4] => 8
[2,-3,-1,4] => 8
[2,-3,-1,-4] => 8
[-2,3,1,4] => 8
[-2,3,1,-4] => 8
[-2,3,-1,4] => 8
[-2,3,-1,-4] => 8
[-2,-3,1,4] => 9
[-2,-3,1,-4] => 7
[-2,-3,-1,4] => 10
[-2,-3,-1,-4] => 7
[2,3,4,1] => 7
[2,3,4,-1] => 7
[2,3,-4,1] => 10
[2,3,-4,-1] => 10
[2,-3,4,1] => 8
[2,-3,4,-1] => 8
[2,-3,-4,1] => 8
[2,-3,-4,-1] => 8
[-2,3,4,1] => 8
[-2,3,4,-1] => 8
[-2,3,-4,1] => 8
[-2,3,-4,-1] => 8
[-2,-3,4,1] => 10
[-2,-3,4,-1] => 10
[-2,-3,-4,1] => 7
[-2,-3,-4,-1] => 7
[2,4,1,3] => 8
[2,4,1,-3] => 8
[2,4,-1,3] => 8
[2,4,-1,-3] => 9
[2,-4,1,3] => 10
[2,-4,1,-3] => 10
[2,-4,-1,3] => 8
[2,-4,-1,-3] => 9
[-2,4,1,3] => 9
[-2,4,1,-3] => 8
[-2,4,-1,3] => 10
[-2,4,-1,-3] => 10
[-2,-4,1,3] => 9
[-2,-4,1,-3] => 8
[-2,-4,-1,3] => 8
[-2,-4,-1,-3] => 8
[2,4,3,1] => 8
[2,4,3,-1] => 8
[2,4,-3,1] => 8
[2,4,-3,-1] => 8
[2,-4,3,1] => 8
[2,-4,3,-1] => 8
[2,-4,-3,1] => 10
[2,-4,-3,-1] => 10
[-2,4,3,1] => 10
[-2,4,3,-1] => 10
[-2,4,-3,1] => 8
[-2,4,-3,-1] => 8
[-2,-4,3,1] => 8
[-2,-4,3,-1] => 8
[-2,-4,-3,1] => 8
[-2,-4,-3,-1] => 8
[3,1,2,4] => 7
[3,1,2,-4] => 10
[3,1,-2,4] => 8
[3,1,-2,-4] => 8
[3,-1,2,4] => 8
[3,-1,2,-4] => 8
[3,-1,-2,4] => 9
[3,-1,-2,-4] => 7
[-3,1,2,4] => 7
[-3,1,2,-4] => 9
[-3,1,-2,4] => 8
[-3,1,-2,-4] => 8
[-3,-1,2,4] => 8
[-3,-1,2,-4] => 8
[-3,-1,-2,4] => 10
[-3,-1,-2,-4] => 7
[3,1,4,2] => 8
[3,1,4,-2] => 8
[3,1,-4,2] => 10
[3,1,-4,-2] => 10
[3,-1,4,2] => 9
[3,-1,4,-2] => 9
[3,-1,-4,2] => 8
[3,-1,-4,-2] => 8
[-3,1,4,2] => 8
[-3,1,4,-2] => 8
[-3,1,-4,2] => 9
[-3,1,-4,-2] => 9
[-3,-1,4,2] => 10
[-3,-1,4,-2] => 10
[-3,-1,-4,2] => 8
[-3,-1,-4,-2] => 8
[3,2,1,4] => 8
[3,2,1,-4] => 6
[3,2,-1,4] => 8
[3,2,-1,-4] => 8
[3,-2,1,4] => 8
[3,-2,1,-4] => 8
[3,-2,-1,4] => 8
[3,-2,-1,-4] => 8
[-3,2,1,4] => 8
[-3,2,1,-4] => 8
[-3,2,-1,4] => 8
[-3,2,-1,-4] => 8
[-3,-2,1,4] => 8
[-3,-2,1,-4] => 8
[-3,-2,-1,4] => 6
[-3,-2,-1,-4] => 8
[3,2,4,1] => 8
[3,2,4,-1] => 8
[3,2,-4,1] => 6
[3,2,-4,-1] => 6
[3,-2,4,1] => 8
[3,-2,4,-1] => 8
[3,-2,-4,1] => 8
[3,-2,-4,-1] => 8
[-3,2,4,1] => 8
[-3,2,4,-1] => 8
[-3,2,-4,1] => 8
[-3,2,-4,-1] => 8
[-3,-2,4,1] => 6
[-3,-2,4,-1] => 6
[-3,-2,-4,1] => 8
[-3,-2,-4,-1] => 8
[3,4,1,2] => 8
[3,4,1,-2] => 8
[3,4,-1,2] => 8
[3,4,-1,-2] => 9
[3,-4,1,2] => 10
[3,-4,1,-2] => 10
[3,-4,-1,2] => 6
[3,-4,-1,-2] => 8
[-3,4,1,2] => 8
[-3,4,1,-2] => 6
[-3,4,-1,2] => 10
[-3,4,-1,-2] => 10
[-3,-4,1,2] => 9
[-3,-4,1,-2] => 8
[-3,-4,-1,2] => 8
[-3,-4,-1,-2] => 8
[3,4,2,1] => 8
[3,4,2,-1] => 8
[3,4,-2,1] => 8
[3,4,-2,-1] => 8
[3,-4,2,1] => 6
[3,-4,2,-1] => 6
[3,-4,-2,1] => 10
[3,-4,-2,-1] => 10
[-3,4,2,1] => 10
[-3,4,2,-1] => 10
[-3,4,-2,1] => 6
[-3,4,-2,-1] => 6
[-3,-4,2,1] => 8
[-3,-4,2,-1] => 8
[-3,-4,-2,1] => 8
[-3,-4,-2,-1] => 8
[4,1,2,3] => 7
[4,1,2,-3] => 10
[4,1,-2,3] => 8
[4,1,-2,-3] => 8
[4,-1,2,3] => 8
[4,-1,2,-3] => 8
[4,-1,-2,3] => 10
[4,-1,-2,-3] => 5
[-4,1,2,3] => 5
[-4,1,2,-3] => 10
[-4,1,-2,3] => 8
[-4,1,-2,-3] => 8
[-4,-1,2,3] => 8
[-4,-1,2,-3] => 8
[-4,-1,-2,3] => 10
[-4,-1,-2,-3] => 7
[4,1,3,2] => 8
[4,1,3,-2] => 8
[4,1,-3,2] => 10
[4,1,-3,-2] => 10
[4,-1,3,2] => 10
[4,-1,3,-2] => 10
[4,-1,-3,2] => 8
[4,-1,-3,-2] => 8
[-4,1,3,2] => 8
[-4,1,3,-2] => 8
[-4,1,-3,2] => 10
[-4,1,-3,-2] => 10
[-4,-1,3,2] => 10
[-4,-1,3,-2] => 10
[-4,-1,-3,2] => 8
[-4,-1,-3,-2] => 8
[4,2,1,3] => 8
[4,2,1,-3] => 6
[4,2,-1,3] => 8
[4,2,-1,-3] => 8
[4,-2,1,3] => 8
[4,-2,1,-3] => 8
[4,-2,-1,3] => 6
[4,-2,-1,-3] => 8
[-4,2,1,3] => 8
[-4,2,1,-3] => 6
[-4,2,-1,3] => 8
[-4,2,-1,-3] => 8
[-4,-2,1,3] => 8
[-4,-2,1,-3] => 8
[-4,-2,-1,3] => 6
[-4,-2,-1,-3] => 8
[4,2,3,1] => 8
[4,2,3,-1] => 8
[4,2,-3,1] => 6
[4,2,-3,-1] => 6
[4,-2,3,1] => 6
[4,-2,3,-1] => 6
[4,-2,-3,1] => 8
[4,-2,-3,-1] => 8
[-4,2,3,1] => 8
[-4,2,3,-1] => 8
[-4,2,-3,1] => 6
[-4,2,-3,-1] => 6
[-4,-2,3,1] => 6
[-4,-2,3,-1] => 6
[-4,-2,-3,1] => 8
[-4,-2,-3,-1] => 8
[4,3,1,2] => 8
[4,3,1,-2] => 6
[4,3,-1,2] => 10
[4,3,-1,-2] => 10
[4,-3,1,2] => 10
[4,-3,1,-2] => 10
[4,-3,-1,2] => 6
[4,-3,-1,-2] => 8
[-4,3,1,2] => 8
[-4,3,1,-2] => 6
[-4,3,-1,2] => 10
[-4,3,-1,-2] => 10
[-4,-3,1,2] => 10
[-4,-3,1,-2] => 10
[-4,-3,-1,2] => 6
[-4,-3,-1,-2] => 8
[4,3,2,1] => 10
[4,3,2,-1] => 10
[4,3,-2,1] => 6
[4,3,-2,-1] => 6
[4,-3,2,1] => 6
[4,-3,2,-1] => 6
[4,-3,-2,1] => 10
[4,-3,-2,-1] => 10
[-4,3,2,1] => 10
[-4,3,2,-1] => 10
[-4,3,-2,1] => 6
[-4,3,-2,-1] => 6
[-4,-3,2,1] => 6
[-4,-3,2,-1] => 6
[-4,-3,-2,1] => 10
[-4,-3,-2,-1] => 10
-----------------------------------------------------------------------------
Created: Nov 26, 2022 at 23:02 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Nov 26, 2022 at 23:02 by Martin Rubey