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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: St001768
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The number of reduced words of a signed permutation.
This is the number of ways to write a permutation as a minimal length product of simple reflections.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(pi):
return len(pi.reduced_words())
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[-1] => 1
[1,2] => 1
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 2
[2,1] => 1
[2,-1] => 1
[-2,1] => 1
[-2,-1] => 1
[1,2,3] => 1
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 2
[-1,2,3] => 1
[-1,2,-3] => 4
[-1,-2,3] => 14
[-1,-2,-3] => 42
[1,3,2] => 1
[1,3,-2] => 1
[1,-3,2] => 1
[1,-3,-2] => 1
[-1,3,2] => 4
[-1,3,-2] => 9
[-1,-3,2] => 9
[-1,-3,-2] => 16
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 1
[2,-1,-3] => 3
[-2,1,3] => 1
[-2,1,-3] => 3
[-2,-1,3] => 5
[-2,-1,-3] => 12
[2,3,1] => 1
[2,3,-1] => 1
[2,-3,1] => 2
[2,-3,-1] => 2
[-2,3,1] => 3
[-2,3,-1] => 5
[-2,-3,1] => 5
[-2,-3,-1] => 7
[3,1,2] => 1
[3,1,-2] => 2
[3,-1,2] => 3
[3,-1,-2] => 5
[-3,1,2] => 1
[-3,1,-2] => 2
[-3,-1,2] => 5
[-3,-1,-2] => 7
[3,2,1] => 2
[3,2,-1] => 3
[3,-2,1] => 2
[3,-2,-1] => 2
[-3,2,1] => 3
[-3,2,-1] => 5
[-3,-2,1] => 2
[-3,-2,-1] => 2
[1,2,3,4] => 1
[1,2,3,-4] => 1
[1,2,-3,4] => 1
[1,2,-3,-4] => 2
[1,-2,3,4] => 1
[1,-2,3,-4] => 4
[1,-2,-3,4] => 14
[1,-2,-3,-4] => 42
[-1,2,3,4] => 1
[-1,2,3,-4] => 6
[-1,2,-3,4] => 48
[-1,2,-3,-4] => 198
[-1,-2,3,4] => 132
[-1,-2,3,-4] => 858
[-1,-2,-3,4] => 6006
[-1,-2,-3,-4] => 24024
[1,2,4,3] => 1
[1,2,4,-3] => 1
[1,2,-4,3] => 1
[1,2,-4,-3] => 1
[1,-2,4,3] => 4
[1,-2,4,-3] => 9
[1,-2,-4,3] => 9
[1,-2,-4,-3] => 16
[-1,2,4,3] => 6
[-1,2,4,-3] => 20
[-1,2,-4,3] => 20
[-1,2,-4,-3] => 50
[-1,-2,4,3] => 858
[-1,-2,4,-3] => 2860
[-1,-2,-4,3] => 2860
[-1,-2,-4,-3] => 7150
[1,3,2,4] => 1
[1,3,2,-4] => 2
[1,3,-2,4] => 1
[1,3,-2,-4] => 3
[1,-3,2,4] => 1
[1,-3,2,-4] => 3
[1,-3,-2,4] => 5
[1,-3,-2,-4] => 12
[-1,3,2,4] => 6
[-1,3,2,-4] => 40
[-1,3,-2,4] => 90
[-1,3,-2,-4] => 486
[-1,-3,2,4] => 90
[-1,-3,2,-4] => 486
[-1,-3,-2,4] => 1872
[-1,-3,-2,-4] => 6318
[1,3,4,2] => 1
[1,3,4,-2] => 1
[1,3,-4,2] => 2
[1,3,-4,-2] => 2
[1,-3,4,2] => 3
[1,-3,4,-2] => 5
[1,-3,-4,2] => 5
[1,-3,-4,-2] => 7
[-1,3,4,2] => 20
[-1,3,4,-2] => 48
[-1,3,-4,2] => 98
[-1,3,-4,-2] => 198
[-1,-3,4,2] => 486
[-1,-3,4,-2] => 1300
[-1,-3,-4,2] => 1300
[-1,-3,-4,-2] => 2730
[1,4,2,3] => 1
[1,4,2,-3] => 2
[1,4,-2,3] => 3
[1,4,-2,-3] => 5
[1,-4,2,3] => 1
[1,-4,2,-3] => 2
[1,-4,-2,3] => 5
[1,-4,-2,-3] => 7
[-1,4,2,3] => 20
[-1,4,2,-3] => 98
[-1,4,-2,3] => 486
[-1,4,-2,-3] => 1300
[-1,-4,2,3] => 48
[-1,-4,2,-3] => 198
[-1,-4,-2,3] => 1300
[-1,-4,-2,-3] => 2730
[1,4,3,2] => 2
[1,4,3,-2] => 3
[1,4,-3,2] => 2
[1,4,-3,-2] => 2
[1,-4,3,2] => 3
[1,-4,3,-2] => 5
[1,-4,-3,2] => 2
[1,-4,-3,-2] => 2
[-1,4,3,2] => 98
[-1,4,3,-2] => 288
[-1,4,-3,2] => 198
[-1,4,-3,-2] => 352
[-1,-4,3,2] => 288
[-1,-4,3,-2] => 838
[-1,-4,-3,2] => 352
[-1,-4,-3,-2] => 572
[2,1,3,4] => 1
[2,1,3,-4] => 2
[2,1,-3,4] => 4
[2,1,-3,-4] => 10
[2,-1,3,4] => 1
[2,-1,3,-4] => 5
[2,-1,-3,4] => 28
[2,-1,-3,-4] => 100
[-2,1,3,4] => 1
[-2,1,3,-4] => 5
[-2,1,-3,4] => 28
[-2,1,-3,-4] => 100
[-2,-1,3,4] => 42
[-2,-1,3,-4] => 240
[-2,-1,-3,4] => 1274
[-2,-1,-3,-4] => 4550
[2,1,4,3] => 2
[2,1,4,-3] => 3
[2,1,-4,3] => 3
[2,1,-4,-3] => 4
[2,-1,4,3] => 5
[2,-1,4,-3] => 14
[2,-1,-4,3] => 14
[2,-1,-4,-3] => 30
[-2,1,4,3] => 5
[-2,1,4,-3] => 14
[-2,1,-4,3] => 14
[-2,1,-4,-3] => 30
[-2,-1,4,3] => 240
[-2,-1,4,-3] => 702
[-2,-1,-4,3] => 702
[-2,-1,-4,-3] => 1560
[2,3,1,4] => 1
[2,3,1,-4] => 3
[2,3,-1,4] => 1
[2,3,-1,-4] => 4
[2,-3,1,4] => 4
[2,-3,1,-4] => 14
[2,-3,-1,4] => 14
[2,-3,-1,-4] => 42
[-2,3,1,4] => 5
[-2,3,1,-4] => 28
[-2,3,-1,4] => 42
[-2,3,-1,-4] => 198
[-2,-3,1,4] => 42
[-2,-3,1,-4] => 198
[-2,-3,-1,4] => 572
[-2,-3,-1,-4] => 1716
[2,3,4,1] => 1
[2,3,4,-1] => 1
[2,3,-4,1] => 3
[2,3,-4,-1] => 3
[2,-3,4,1] => 9
[2,-3,4,-1] => 14
[2,-3,-4,1] => 21
[2,-3,-4,-1] => 28
[-2,3,4,1] => 14
[-2,3,4,-1] => 28
[-2,3,-4,1] => 58
[-2,3,-4,-1] => 100
[-2,-3,4,1] => 198
[-2,-3,4,-1] => 462
[-2,-3,-4,1] => 462
[-2,-3,-4,-1] => 858
[2,4,1,3] => 2
[2,4,1,-3] => 5
[2,4,-1,3] => 4
[2,4,-1,-3] => 9
[2,-4,1,3] => 3
[2,-4,1,-3] => 7
[2,-4,-1,3] => 9
[2,-4,-1,-3] => 16
[-2,4,1,3] => 14
[-2,4,1,-3] => 58
[-2,4,-1,3] => 198
[-2,4,-1,-3] => 462
[-2,-4,1,3] => 28
[-2,-4,1,-3] => 100
[-2,-4,-1,3] => 462
[-2,-4,-1,-3] => 858
[2,4,3,1] => 3
[2,4,3,-1] => 4
[2,4,-3,1] => 5
[2,4,-3,-1] => 5
[2,-4,3,1] => 6
[2,-4,3,-1] => 9
[2,-4,-3,1] => 7
[2,-4,-3,-1] => 7
[-2,4,3,1] => 58
[-2,4,3,-1] => 142
[-2,4,-3,1] => 100
[-2,4,-3,-1] => 154
[-2,-4,3,1] => 142
[-2,-4,3,-1] => 352
[-2,-4,-3,1] => 154
[-2,-4,-3,-1] => 220
[3,1,2,4] => 1
[3,1,2,-4] => 3
[3,1,-2,4] => 4
[3,1,-2,-4] => 14
[3,-1,2,4] => 5
[3,-1,2,-4] => 28
[3,-1,-2,4] => 42
[3,-1,-2,-4] => 198
[-3,1,2,4] => 1
[-3,1,2,-4] => 4
[-3,1,-2,4] => 14
[-3,1,-2,-4] => 42
[-3,-1,2,4] => 42
[-3,-1,2,-4] => 198
[-3,-1,-2,4] => 572
[-3,-1,-2,-4] => 1716
[3,1,4,2] => 2
[3,1,4,-2] => 3
[3,1,-4,2] => 5
[3,1,-4,-2] => 7
[3,-1,4,2] => 14
[3,-1,4,-2] => 28
[3,-1,-4,2] => 58
[3,-1,-4,-2] => 100
[-3,1,4,2] => 4
[-3,1,4,-2] => 9
[-3,1,-4,2] => 9
[-3,1,-4,-2] => 16
[-3,-1,4,2] => 198
[-3,-1,4,-2] => 462
[-3,-1,-4,2] => 462
[-3,-1,-4,-2] => 858
[3,2,1,4] => 2
[3,2,1,-4] => 8
[3,2,-1,4] => 5
[3,2,-1,-4] => 23
[3,-2,1,4] => 4
[3,-2,1,-4] => 18
[3,-2,-1,4] => 14
[3,-2,-1,-4] => 56
[-3,2,1,4] => 5
[-3,2,1,-4] => 23
[-3,2,-1,4] => 42
[-3,2,-1,-4] => 156
[-3,-2,1,4] => 14
[-3,-2,1,-4] => 56
[-3,-2,-1,4] => 110
[-3,-2,-1,-4] => 286
[3,2,4,1] => 3
[3,2,4,-1] => 4
[3,2,-4,1] => 11
[3,2,-4,-1] => 14
[3,-2,4,1] => 9
[3,-2,4,-1] => 14
[3,-2,-4,1] => 30
[3,-2,-4,-1] => 42
[-3,2,4,1] => 14
[-3,2,4,-1] => 28
[-3,2,-4,1] => 44
[-3,2,-4,-1] => 72
[-3,-2,4,1] => 56
[-3,-2,4,-1] => 110
[-3,-2,-4,1] => 110
[-3,-2,-4,-1] => 176
[3,4,1,2] => 2
[3,4,1,-2] => 5
[3,4,-1,2] => 9
[3,4,-1,-2] => 14
[3,-4,1,2] => 5
[3,-4,1,-2] => 12
[3,-4,-1,2] => 30
[3,-4,-1,-2] => 42
[-3,4,1,2] => 9
[-3,4,1,-2] => 30
[-3,4,-1,2] => 156
[-3,4,-1,-2] => 264
[-3,-4,1,2] => 14
[-3,-4,1,-2] => 42
[-3,-4,-1,2] => 264
[-3,-4,-1,-2] => 396
[3,4,2,1] => 5
[3,4,2,-1] => 9
[3,4,-2,1] => 5
[3,4,-2,-1] => 5
[3,-4,2,1] => 16
[3,-4,2,-1] => 30
[3,-4,-2,1] => 12
[3,-4,-2,-1] => 12
[-3,4,2,1] => 44
[-3,4,2,-1] => 114
[-3,4,-2,1] => 42
[-3,4,-2,-1] => 54
[-3,-4,2,1] => 84
[-3,-4,2,-1] => 210
[-3,-4,-2,1] => 54
[-3,-4,-2,-1] => 66
[4,1,2,3] => 1
[4,1,2,-3] => 3
[4,1,-2,3] => 9
[4,1,-2,-3] => 21
[4,-1,2,3] => 14
[4,-1,2,-3] => 58
[4,-1,-2,3] => 198
[4,-1,-2,-3] => 462
[-4,1,2,3] => 1
[-4,1,2,-3] => 3
[-4,1,-2,3] => 14
[-4,1,-2,-3] => 28
[-4,-1,2,3] => 28
[-4,-1,2,-3] => 100
[-4,-1,-2,3] => 462
[-4,-1,-2,-3] => 858
[4,1,3,2] => 3
[4,1,3,-2] => 6
[4,1,-3,2] => 5
[4,1,-3,-2] => 7
[4,-1,3,2] => 58
[4,-1,3,-2] => 142
[4,-1,-3,2] => 100
[4,-1,-3,-2] => 154
[-4,1,3,2] => 4
[-4,1,3,-2] => 9
[-4,1,-3,2] => 5
[-4,1,-3,-2] => 7
[-4,-1,3,2] => 142
[-4,-1,3,-2] => 352
[-4,-1,-3,2] => 154
[-4,-1,-3,-2] => 220
[4,2,1,3] => 3
[4,2,1,-3] => 11
[4,2,-1,3] => 14
[4,2,-1,-3] => 44
[4,-2,1,3] => 9
[4,-2,1,-3] => 30
[4,-2,-1,3] => 56
[4,-2,-1,-3] => 110
[-4,2,1,3] => 4
[-4,2,1,-3] => 14
[-4,2,-1,3] => 28
[-4,2,-1,-3] => 72
[-4,-2,1,3] => 14
[-4,-2,1,-3] => 42
[-4,-2,-1,3] => 110
[-4,-2,-1,-3] => 176
[4,2,3,1] => 6
[4,2,3,-1] => 10
[4,2,-3,1] => 16
[4,2,-3,-1] => 21
[4,-2,3,1] => 30
[4,-2,3,-1] => 56
[4,-2,-3,1] => 42
[4,-2,-3,-1] => 54
[-4,2,3,1] => 10
[-4,2,3,-1] => 19
[-4,2,-3,1] => 21
[-4,2,-3,-1] => 28
[-4,-2,3,1] => 56
[-4,-2,3,-1] => 110
[-4,-2,-3,1] => 54
[-4,-2,-3,-1] => 66
[4,3,1,2] => 5
[4,3,1,-2] => 16
[4,3,-1,2] => 44
[4,3,-1,-2] => 84
[4,-3,1,2] => 5
[4,-3,1,-2] => 12
[4,-3,-1,2] => 42
[4,-3,-1,-2] => 54
[-4,3,1,2] => 9
[-4,3,1,-2] => 30
[-4,3,-1,2] => 114
[-4,3,-1,-2] => 210
[-4,-3,1,2] => 5
[-4,-3,1,-2] => 12
[-4,-3,-1,2] => 54
[-4,-3,-1,-2] => 66
[4,3,2,1] => 16
[4,3,2,-1] => 35
[4,3,-2,1] => 21
[4,3,-2,-1] => 26
[4,-3,2,1] => 21
[4,-3,2,-1] => 42
[4,-3,-2,1] => 12
[4,-3,-2,-1] => 12
[-4,3,2,1] => 35
[-4,3,2,-1] => 84
[-4,3,-2,1] => 42
[-4,3,-2,-1] => 54
[-4,-3,2,1] => 26
[-4,-3,2,-1] => 54
[-4,-3,-2,1] => 12
[-4,-3,-2,-1] => 12
-----------------------------------------------------------------------------
Created: Feb 04, 2022 at 13:13 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Feb 04, 2022 at 13:13 by Martin Rubey