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Identifier
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
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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.
Code
def statistic(pi):
    return len(pi.reduced_words())
Created
Feb 04, 2022 at 13:13 by Martin Rubey
Updated
Feb 04, 2022 at 13:13 by Martin Rubey