Identifier
Values
=>
[1]=>1
[-1]=>1
[1,2]=>1
[1,-2]=>2
[-1,2]=>1
[-1,-2]=>1
[2,1]=>2
[2,-1]=>1
[-2,1]=>3
[-2,-1]=>1
[1,2,3]=>1
[1,2,-3]=>3
[1,-2,3]=>4
[1,-2,-3]=>6
[-1,2,3]=>1
[-1,2,-3]=>2
[-1,-2,3]=>1
[-1,-2,-3]=>1
[1,3,2]=>3
[1,3,-2]=>3
[1,-3,2]=>6
[1,-3,-2]=>4
[-1,3,2]=>2
[-1,3,-2]=>1
[-1,-3,2]=>3
[-1,-3,-2]=>1
[2,1,3]=>3
[2,1,-3]=>9
[2,-1,3]=>1
[2,-1,-3]=>2
[-2,1,3]=>5
[-2,1,-3]=>8
[-2,-1,3]=>1
[-2,-1,-3]=>1
[2,3,1]=>3
[2,3,-1]=>1
[2,-3,1]=>8
[2,-3,-1]=>2
[-2,3,1]=>8
[-2,3,-1]=>2
[-2,-3,1]=>10
[-2,-3,-1]=>2
[3,1,2]=>6
[3,1,-2]=>8
[3,-1,2]=>2
[3,-1,-2]=>1
[-3,1,2]=>10
[-3,1,-2]=>10
[-3,-1,2]=>3
[-3,-1,-2]=>1
[3,2,1]=>8
[3,2,-1]=>3
[3,-2,1]=>6
[3,-2,-1]=>1
[-3,2,1]=>15
[-3,2,-1]=>5
[-3,-2,1]=>7
[-3,-2,-1]=>1
[1,2,3,4]=>1
[1,2,3,-4]=>4
[1,2,-3,4]=>10
[1,2,-3,-4]=>20
[1,-2,3,4]=>6
[1,-2,3,-4]=>16
[1,-2,-3,4]=>15
[1,-2,-3,-4]=>20
[-1,2,3,4]=>1
[-1,2,3,-4]=>3
[-1,2,-3,4]=>4
[-1,2,-3,-4]=>6
[-1,-2,3,4]=>1
[-1,-2,3,-4]=>2
[-1,-2,-3,4]=>1
[-1,-2,-3,-4]=>1
[1,2,4,3]=>4
[1,2,4,-3]=>6
[1,2,-4,3]=>10
[1,2,-4,-3]=>10
[1,-2,4,3]=>16
[1,-2,4,-3]=>13
[1,-2,-4,3]=>29
[1,-2,-4,-3]=>16
[-1,2,4,3]=>3
[-1,2,4,-3]=>3
[-1,2,-4,3]=>6
[-1,2,-4,-3]=>4
[-1,-2,4,3]=>2
[-1,-2,4,-3]=>1
[-1,-2,-4,3]=>3
[-1,-2,-4,-3]=>1
[1,3,2,4]=>4
[1,3,2,-4]=>16
[1,3,-2,4]=>5
[1,3,-2,-4]=>13
[1,-3,2,4]=>15
[1,-3,2,-4]=>33
[1,-3,-2,4]=>11
[1,-3,-2,-4]=>14
[-1,3,2,4]=>3
[-1,3,2,-4]=>9
[-1,3,-2,4]=>1
[-1,3,-2,-4]=>2
[-1,-3,2,4]=>5
[-1,-3,2,-4]=>8
[-1,-3,-2,4]=>1
[-1,-3,-2,-4]=>1
[1,3,4,2]=>6
[1,3,4,-2]=>4
[1,3,-4,2]=>20
[1,3,-4,-2]=>10
[1,-3,4,2]=>33
[1,-3,4,-2]=>17
[1,-3,-4,2]=>50
[1,-3,-4,-2]=>20
[-1,3,4,2]=>3
[-1,3,4,-2]=>1
[-1,3,-4,2]=>8
[-1,3,-4,-2]=>2
[-1,-3,4,2]=>8
[-1,-3,4,-2]=>2
[-1,-3,-4,2]=>10
[-1,-3,-4,-2]=>2
[1,4,2,3]=>10
[1,4,2,-3]=>20
[1,4,-2,3]=>13
[1,4,-2,-3]=>10
[1,-4,2,3]=>20
[1,-4,2,-3]=>30
[1,-4,-2,3]=>23
[1,-4,-2,-3]=>12
[-1,4,2,3]=>6
[-1,4,2,-3]=>8
[-1,4,-2,3]=>2
[-1,4,-2,-3]=>1
[-1,-4,2,3]=>10
[-1,-4,2,-3]=>10
[-1,-4,-2,3]=>3
[-1,-4,-2,-3]=>1
[1,4,3,2]=>20
[1,4,3,-2]=>15
[1,4,-3,2]=>20
[1,4,-3,-2]=>7
[1,-4,3,2]=>45
[1,-4,3,-2]=>30
[1,-4,-3,2]=>27
[1,-4,-3,-2]=>8
[-1,4,3,2]=>8
[-1,4,3,-2]=>3
[-1,4,-3,2]=>6
[-1,4,-3,-2]=>1
[-1,-4,3,2]=>15
[-1,-4,3,-2]=>5
[-1,-4,-3,2]=>7
[-1,-4,-3,-2]=>1
[2,1,3,4]=>4
[2,1,3,-4]=>16
[2,1,-3,4]=>40
[2,1,-3,-4]=>80
[2,-1,3,4]=>1
[2,-1,3,-4]=>3
[2,-1,-3,4]=>4
[2,-1,-3,-4]=>6
[-2,1,3,4]=>7
[-2,1,3,-4]=>19
[-2,1,-3,4]=>19
[-2,1,-3,-4]=>26
[-2,-1,3,4]=>1
[-2,-1,3,-4]=>2
[-2,-1,-3,4]=>1
[-2,-1,-3,-4]=>1
[2,1,4,3]=>16
[2,1,4,-3]=>24
[2,1,-4,3]=>40
[2,1,-4,-3]=>40
[2,-1,4,3]=>3
[2,-1,4,-3]=>3
[2,-1,-4,3]=>6
[2,-1,-4,-3]=>4
[-2,1,4,3]=>19
[-2,1,4,-3]=>16
[-2,1,-4,3]=>35
[-2,1,-4,-3]=>20
[-2,-1,4,3]=>2
[-2,-1,4,-3]=>1
[-2,-1,-4,3]=>3
[-2,-1,-4,-3]=>1
[2,3,1,4]=>6
[2,3,1,-4]=>24
[2,3,-1,4]=>1
[2,3,-1,-4]=>3
[2,-3,1,4]=>39
[2,-3,1,-4]=>83
[2,-3,-1,4]=>4
[2,-3,-1,-4]=>6
[-2,3,1,4]=>19
[-2,3,1,-4]=>51
[-2,3,-1,4]=>2
[-2,3,-1,-4]=>4
[-2,-3,1,4]=>21
[-2,-3,1,-4]=>30
[-2,-3,-1,4]=>2
[-2,-3,-1,-4]=>2
[2,3,4,1]=>4
[2,3,4,-1]=>1
[2,3,-4,1]=>15
[2,3,-4,-1]=>3
[2,-3,4,1]=>33
[2,-3,4,-1]=>7
[2,-3,-4,1]=>60
[2,-3,-4,-1]=>10
[-2,3,4,1]=>16
[-2,3,4,-1]=>3
[-2,3,-4,1]=>39
[-2,3,-4,-1]=>6
[-2,-3,4,1]=>30
[-2,-3,4,-1]=>5
[-2,-3,-4,1]=>35
[-2,-3,-4,-1]=>5
[2,4,1,3]=>20
[2,4,1,-3]=>35
[2,4,-1,3]=>3
[2,4,-1,-3]=>3
[2,-4,1,3]=>45
[2,-4,1,-3]=>57
[2,-4,-1,3]=>6
[2,-4,-1,-3]=>4
[-2,4,1,3]=>35
[-2,4,1,-3]=>39
[-2,4,-1,3]=>4
[-2,4,-1,-3]=>2
[-2,-4,1,3]=>54
[-2,-4,1,-3]=>46
[-2,-4,-1,3]=>6
[-2,-4,-1,-3]=>2
[2,4,3,1]=>15
[2,4,3,-1]=>4
[2,4,-3,1]=>20
[2,4,-3,-1]=>3
[2,-4,3,1]=>36
[2,-4,3,-1]=>9
[2,-4,-3,1]=>31
[2,-4,-3,-1]=>4
[-2,4,3,1]=>39
[-2,4,3,-1]=>8
[-2,4,-3,1]=>26
[-2,4,-3,-1]=>3
[-2,-4,3,1]=>67
[-2,-4,3,-1]=>13
[-2,-4,-3,1]=>29
[-2,-4,-3,-1]=>3
[3,1,2,4]=>10
[3,1,2,-4]=>40
[3,1,-2,4]=>19
[3,1,-2,-4]=>49
[3,-1,2,4]=>3
[3,-1,2,-4]=>9
[3,-1,-2,4]=>1
[3,-1,-2,-4]=>2
[-3,1,2,4]=>21
[-3,1,2,-4]=>49
[-3,1,-2,4]=>26
[-3,1,-2,-4]=>34
[-3,-1,2,4]=>5
[-3,-1,2,-4]=>8
[-3,-1,-2,4]=>1
[-3,-1,-2,-4]=>1
[3,1,4,2]=>20
[3,1,4,-2]=>15
[3,1,-4,2]=>65
[3,1,-4,-2]=>37
[3,-1,4,2]=>3
[3,-1,4,-2]=>1
[3,-1,-4,2]=>8
[3,-1,-4,-2]=>2
[-3,1,4,2]=>49
[-3,1,4,-2]=>30
[-3,1,-4,2]=>79
[-3,1,-4,-2]=>36
[-3,-1,4,2]=>8
[-3,-1,4,-2]=>2
[-3,-1,-4,2]=>10
[-3,-1,-4,-2]=>2
[3,2,1,4]=>20
[3,2,1,-4]=>80
[3,2,-1,4]=>4
[3,2,-1,-4]=>12
[3,-2,1,4]=>16
[3,-2,1,-4]=>42
[3,-2,-1,4]=>1
[3,-2,-1,-4]=>2
[-3,2,1,4]=>56
[-3,2,1,-4]=>128
[-3,2,-1,4]=>9
[-3,2,-1,-4]=>14
[-3,-2,1,4]=>16
[-3,-2,1,-4]=>22
[-3,-2,-1,4]=>1
[-3,-2,-1,-4]=>1
[3,2,4,1]=>15
[3,2,4,-1]=>4
[3,2,-4,1]=>56
[3,2,-4,-1]=>12
[3,-2,4,1]=>13
[3,-2,4,-1]=>2
[3,-2,-4,1]=>31
[3,-2,-4,-1]=>4
[-3,2,4,1]=>49
[-3,2,4,-1]=>12
[-3,2,-4,1]=>97
[-3,2,-4,-1]=>18
[-3,-2,4,1]=>22
[-3,-2,4,-1]=>3
[-3,-2,-4,1]=>25
[-3,-2,-4,-1]=>3
[3,4,1,2]=>20
[3,4,1,-2]=>20
[3,4,-1,2]=>3
[3,4,-1,-2]=>1
[3,-4,1,2]=>60
[3,-4,1,-2]=>48
[3,-4,-1,2]=>8
[3,-4,-1,-2]=>2
[-3,4,1,2]=>79
[-3,4,1,-2]=>62
[-3,4,-1,2]=>14
[-3,4,-1,-2]=>3
[-3,-4,1,2]=>105
[-3,-4,1,-2]=>70
[-3,-4,-1,2]=>17
[-3,-4,-1,-2]=>3
[3,4,2,1]=>20
[3,4,2,-1]=>6
[3,4,-2,1]=>10
[3,4,-2,-1]=>1
[3,-4,2,1]=>64
[3,-4,2,-1]=>17
[3,-4,-2,1]=>23
[3,-4,-2,-1]=>2
[-3,4,2,1]=>97
[-3,4,2,-1]=>27
[-3,4,-2,1]=>34
[-3,4,-2,-1]=>3
[-3,-4,2,1]=>140
[-3,-4,2,-1]=>35
[-3,-4,-2,1]=>37
[-3,-4,-2,-1]=>3
[4,1,2,3]=>20
[4,1,2,-3]=>45
[4,1,-2,3]=>39
[4,1,-2,-3]=>36
[4,-1,2,3]=>6
[4,-1,2,-3]=>8
[4,-1,-2,3]=>2
[4,-1,-2,-3]=>1
[-4,1,2,3]=>35
[-4,1,2,-3]=>63
[-4,1,-2,3]=>63
[-4,1,-2,-3]=>42
[-4,-1,2,3]=>10
[-4,-1,2,-3]=>10
[-4,-1,-2,3]=>3
[-4,-1,-2,-3]=>1
[4,1,3,2]=>45
[4,1,3,-2]=>36
[4,1,-3,2]=>60
[4,1,-3,-2]=>25
[4,-1,3,2]=>8
[4,-1,3,-2]=>3
[4,-1,-3,2]=>6
[4,-1,-3,-2]=>1
[-4,1,3,2]=>84
[-4,1,3,-2]=>63
[-4,1,-3,2]=>77
[-4,1,-3,-2]=>28
[-4,-1,3,2]=>15
[-4,-1,3,-2]=>5
[-4,-1,-3,2]=>7
[-4,-1,-3,-2]=>1
[4,2,1,3]=>45
[4,2,1,-3]=>96
[4,2,-1,3]=>9
[4,2,-1,-3]=>11
[4,-2,1,3]=>29
[4,-2,1,-3]=>31
[4,-2,-1,3]=>2
[4,-2,-1,-3]=>1
[-4,2,1,3]=>84
[-4,2,1,-3]=>140
[-4,2,-1,3]=>16
[-4,2,-1,-3]=>14
[-4,-2,1,3]=>44
[-4,-2,1,-3]=>36
[-4,-2,-1,3]=>3
[-4,-2,-1,-3]=>1
[4,2,3,1]=>36
[4,2,3,-1]=>10
[4,2,-3,1]=>64
[4,2,-3,-1]=>11
[4,-2,3,1]=>31
[4,-2,3,-1]=>5
[4,-2,-3,1]=>20
[4,-2,-3,-1]=>2
[-4,2,3,1]=>70
[-4,2,3,-1]=>19
[-4,2,-3,1]=>91
[-4,2,-3,-1]=>14
[-4,-2,3,1]=>52
[-4,-2,3,-1]=>8
[-4,-2,-3,1]=>22
[-4,-2,-3,-1]=>2
[4,3,1,2]=>60
[4,3,1,-2]=>64
[4,3,-1,2]=>11
[4,3,-1,-2]=>4
[4,-3,1,2]=>50
[4,-3,1,-2]=>31
[4,-3,-1,2]=>6
[4,-3,-1,-2]=>1
[-4,3,1,2]=>126
[-4,3,1,-2]=>121
[-4,3,-1,2]=>23
[-4,3,-1,-2]=>7
[-4,-3,1,2]=>61
[-4,-3,1,-2]=>34
[-4,-3,-1,2]=>7
[-4,-3,-1,-2]=>1
[4,3,2,1]=>64
[4,3,2,-1]=>20
[4,3,-2,1]=>36
[4,3,-2,-1]=>4
[4,-3,2,1]=>60
[4,-3,2,-1]=>14
[4,-3,-2,1]=>14
[4,-3,-2,-1]=>1
[-4,3,2,1]=>140
[-4,3,2,-1]=>42
[-4,3,-2,1]=>68
[-4,3,-2,-1]=>7
[-4,-3,2,1]=>78
[-4,-3,2,-1]=>17
[-4,-3,-2,1]=>15
[-4,-3,-2,-1]=>1
[1,2,3,4,5]=>1
[1,2,3,4,-5]=>5
[1,2,3,-4,5]=>20
[1,2,3,-4,-5]=>50
[1,2,-3,4,5]=>21
[1,2,-3,4,-5]=>70
[1,2,-3,-4,5]=>105
[1,2,-3,-4,-5]=>175
[1,-2,3,4,5]=>8
[1,-2,3,4,-5]=>30
[1,-2,3,-4,5]=>64
[1,-2,3,-4,-5]=>120
[1,-2,-3,4,5]=>28
[1,-2,-3,4,-5]=>70
[1,-2,-3,-4,5]=>56
[1,-2,-3,-4,-5]=>70
[-1,2,3,4,5]=>1
[-1,2,3,4,-5]=>4
[-1,2,3,-4,5]=>10
[-1,2,3,-4,-5]=>20
[-1,2,-3,4,5]=>6
[-1,2,-3,4,-5]=>16
[-1,2,-3,-4,5]=>15
[-1,2,-3,-4,-5]=>20
[-1,-2,3,4,5]=>1
[-1,-2,3,4,-5]=>3
[-1,-2,3,-4,5]=>4
[-1,-2,3,-4,-5]=>6
[-1,-2,-3,4,5]=>1
[-1,-2,-3,4,-5]=>2
[-1,-2,-3,-4,5]=>1
[-1,-2,-3,-4,-5]=>1
[1,2,3,5,4]=>5
[1,2,3,5,-4]=>10
[1,2,3,-5,4]=>15
[1,2,3,-5,-4]=>20
[1,2,-3,5,4]=>70
[1,2,-3,5,-4]=>79
[1,2,-3,-5,4]=>149
[1,2,-3,-5,-4]=>115
[1,-2,3,5,4]=>30
[1,-2,3,5,-4]=>41
[1,-2,3,-5,4]=>71
[1,-2,3,-5,-4]=>65
[1,-2,-3,5,4]=>70
[1,-2,-3,5,-4]=>51
[1,-2,-3,-5,4]=>121
[1,-2,-3,-5,-4]=>60
[-1,2,3,5,4]=>4
[-1,2,3,5,-4]=>6
[-1,2,3,-5,4]=>10
[-1,2,3,-5,-4]=>10
[-1,2,-3,5,4]=>16
[-1,2,-3,5,-4]=>13
[-1,2,-3,-5,4]=>29
[-1,2,-3,-5,-4]=>16
[-1,-2,3,5,4]=>3
[-1,-2,3,5,-4]=>3
[-1,-2,3,-5,4]=>6
[-1,-2,3,-5,-4]=>4
[-1,-2,-3,5,4]=>2
[-1,-2,-3,5,-4]=>1
[-1,-2,-3,-5,4]=>3
[-1,-2,-3,-5,-4]=>1
[1,2,4,3,5]=>5
[1,2,4,3,-5]=>25
[1,2,4,-3,5]=>15
[1,2,4,-3,-5]=>48
[1,2,-4,3,5]=>35
[1,2,-4,3,-5]=>98
[1,2,-4,-3,5]=>61
[1,2,-4,-3,-5]=>95
[1,-2,4,3,5]=>30
[1,-2,4,3,-5]=>112
[1,-2,4,-3,5]=>26
[1,-2,4,-3,-5]=>64
[1,-2,-4,3,5]=>90
[1,-2,-4,3,-5]=>184
[1,-2,-4,-3,5]=>48
[1,-2,-4,-3,-5]=>58
[-1,2,4,3,5]=>4
[-1,2,4,3,-5]=>16
[-1,2,4,-3,5]=>5
[-1,2,4,-3,-5]=>13
[-1,2,-4,3,5]=>15
[-1,2,-4,3,-5]=>33
[-1,2,-4,-3,5]=>11
[-1,2,-4,-3,-5]=>14
[-1,-2,4,3,5]=>3
[-1,-2,4,3,-5]=>9
[-1,-2,4,-3,5]=>1
[-1,-2,4,-3,-5]=>2
[-1,-2,-4,3,5]=>5
[-1,-2,-4,3,-5]=>8
[-1,-2,-4,-3,5]=>1
[-1,-2,-4,-3,-5]=>1
[1,2,4,5,3]=>10
[1,2,4,5,-3]=>10
[1,2,4,-5,3]=>40
[1,2,4,-5,-3]=>30
[1,2,-4,5,3]=>98
[1,2,-4,5,-3]=>77
[1,2,-4,-5,3]=>175
[1,2,-4,-5,-3]=>105
[1,-2,4,5,3]=>41
[1,-2,4,5,-3]=>23
[1,-2,4,-5,3]=>129
[1,-2,4,-5,-3]=>55
[1,-2,-4,5,3]=>184
[1,-2,-4,5,-3]=>81
[1,-2,-4,-5,3]=>265
[1,-2,-4,-5,-3]=>92
[-1,2,4,5,3]=>6
[-1,2,4,5,-3]=>4
[-1,2,4,-5,3]=>20
[-1,2,4,-5,-3]=>10
[-1,2,-4,5,3]=>33
[-1,2,-4,5,-3]=>17
[-1,2,-4,-5,3]=>50
[-1,2,-4,-5,-3]=>20
[-1,-2,4,5,3]=>3
[-1,-2,4,5,-3]=>1
[-1,-2,4,-5,3]=>8
[-1,-2,4,-5,-3]=>2
[-1,-2,-4,5,3]=>8
[-1,-2,-4,5,-3]=>2
[-1,-2,-4,-5,3]=>10
[-1,-2,-4,-5,-3]=>2
[1,2,5,3,4]=>15
[1,2,5,3,-4]=>40
[1,2,5,-3,4]=>48
[1,2,5,-3,-4]=>50
[1,2,-5,3,4]=>35
[1,2,-5,3,-4]=>70
[1,2,-5,-3,4]=>98
[1,2,-5,-3,-4]=>70
[1,-2,5,3,4]=>71
[1,-2,5,3,-4]=>129
[1,-2,5,-3,4]=>64
[1,-2,5,-3,-4]=>45
[1,-2,-5,3,4]=>135
[1,-2,-5,3,-4]=>185
[1,-2,-5,-3,4]=>109
[1,-2,-5,-3,-4]=>52
[-1,2,5,3,4]=>10
[-1,2,5,3,-4]=>20
[-1,2,5,-3,4]=>13
[-1,2,5,-3,-4]=>10
[-1,2,-5,3,4]=>20
[-1,2,-5,3,-4]=>30
[-1,2,-5,-3,4]=>23
[-1,2,-5,-3,-4]=>12
[-1,-2,5,3,4]=>6
[-1,-2,5,3,-4]=>8
[-1,-2,5,-3,4]=>2
[-1,-2,5,-3,-4]=>1
[-1,-2,-5,3,4]=>10
[-1,-2,-5,3,-4]=>10
[-1,-2,-5,-3,4]=>3
[-1,-2,-5,-3,-4]=>1
[1,2,5,4,3]=>40
[1,2,5,4,-3]=>45
[1,2,5,-4,3]=>50
[1,2,5,-4,-3]=>27
[1,2,-5,4,3]=>105
[1,2,-5,4,-3]=>105
[1,2,-5,-4,3]=>77
[1,2,-5,-4,-3]=>35
[1,-2,5,4,3]=>129
[1,-2,5,4,-3]=>81
[1,-2,5,-4,3]=>120
[1,-2,5,-4,-3]=>36
[1,-2,-5,4,3]=>275
[1,-2,-5,4,-3]=>155
[1,-2,-5,-4,3]=>156
[1,-2,-5,-4,-3]=>40
[-1,2,5,4,3]=>20
[-1,2,5,4,-3]=>15
[-1,2,5,-4,3]=>20
[-1,2,5,-4,-3]=>7
[-1,2,-5,4,3]=>45
[-1,2,-5,4,-3]=>30
[-1,2,-5,-4,3]=>27
[-1,2,-5,-4,-3]=>8
[-1,-2,5,4,3]=>8
[-1,-2,5,4,-3]=>3
[-1,-2,5,-4,3]=>6
[-1,-2,5,-4,-3]=>1
[-1,-2,-5,4,3]=>15
[-1,-2,-5,4,-3]=>5
[-1,-2,-5,-4,3]=>7
[-1,-2,-5,-4,-3]=>1
[1,3,2,4,5]=>5
[1,3,2,4,-5]=>25
[1,3,2,-4,5]=>100
[1,3,2,-4,-5]=>250
[1,3,-2,4,5]=>7
[1,3,-2,4,-5]=>26
[1,3,-2,-4,5]=>54
[1,3,-2,-4,-5]=>100
[1,-3,2,4,5]=>28
[1,-3,2,4,-5]=>96
[1,-3,2,-4,5]=>159
[1,-3,2,-4,-5]=>275
[1,-3,-2,4,5]=>22
[1,-3,-2,4,-5]=>54
[1,-3,-2,-4,5]=>41
[1,-3,-2,-4,-5]=>50
[-1,3,2,4,5]=>4
[-1,3,2,4,-5]=>16
[-1,3,2,-4,5]=>40
[-1,3,2,-4,-5]=>80
[-1,3,-2,4,5]=>1
[-1,3,-2,4,-5]=>3
[-1,3,-2,-4,5]=>4
[-1,3,-2,-4,-5]=>6
[-1,-3,2,4,5]=>7
[-1,-3,2,4,-5]=>19
[-1,-3,2,-4,5]=>19
[-1,-3,2,-4,-5]=>26
[-1,-3,-2,4,5]=>1
[-1,-3,-2,4,-5]=>2
[-1,-3,-2,-4,5]=>1
[-1,-3,-2,-4,-5]=>1
[1,3,2,5,4]=>25
[1,3,2,5,-4]=>50
[1,3,2,-5,4]=>75
[1,3,2,-5,-4]=>100
[1,3,-2,5,4]=>26
[1,3,-2,5,-4]=>35
[1,3,-2,-5,4]=>61
[1,3,-2,-5,-4]=>55
[1,-3,2,5,4]=>96
[1,-3,2,5,-4]=>114
[1,-3,2,-5,4]=>210
[1,-3,2,-5,-4]=>170
[1,-3,-2,5,4]=>54
[1,-3,-2,5,-4]=>38
[1,-3,-2,-5,4]=>92
[1,-3,-2,-5,-4]=>44
[-1,3,2,5,4]=>16
[-1,3,2,5,-4]=>24
[-1,3,2,-5,4]=>40
[-1,3,2,-5,-4]=>40
[-1,3,-2,5,4]=>3
[-1,3,-2,5,-4]=>3
[-1,3,-2,-5,4]=>6
[-1,3,-2,-5,-4]=>4
[-1,-3,2,5,4]=>19
[-1,-3,2,5,-4]=>16
[-1,-3,2,-5,4]=>35
[-1,-3,2,-5,-4]=>20
[-1,-3,-2,5,4]=>2
[-1,-3,-2,5,-4]=>1
[-1,-3,-2,-5,4]=>3
[-1,-3,-2,-5,-4]=>1
[1,3,4,2,5]=>10
[1,3,4,2,-5]=>50
[1,3,4,-2,5]=>6
[1,3,4,-2,-5]=>22
[1,3,-4,2,5]=>119
[1,3,-4,2,-5]=>322
[1,3,-4,-2,5]=>44
[1,3,-4,-2,-5]=>80
[1,-3,4,2,5]=>96
[1,-3,4,2,-5]=>324
[1,-3,4,-2,5]=>37
[1,-3,4,-2,-5]=>89
[1,-3,-4,2,5]=>196
[1,-3,-4,2,-5]=>364
[1,-3,-4,-2,5]=>63
[1,-3,-4,-2,-5]=>74
[-1,3,4,2,5]=>6
[-1,3,4,2,-5]=>24
[-1,3,4,-2,5]=>1
[-1,3,4,-2,-5]=>3
[-1,3,-4,2,5]=>39
[-1,3,-4,2,-5]=>83
[-1,3,-4,-2,5]=>4
[-1,3,-4,-2,-5]=>6
[-1,-3,4,2,5]=>19
[-1,-3,4,2,-5]=>51
[-1,-3,4,-2,5]=>2
[-1,-3,4,-2,-5]=>4
[-1,-3,-4,2,5]=>21
[-1,-3,-4,2,-5]=>30
[-1,-3,-4,-2,5]=>2
[-1,-3,-4,-2,-5]=>2
[1,3,4,5,2]=>10
[1,3,4,5,-2]=>5
[1,3,4,-5,2]=>45
[1,3,4,-5,-2]=>18
[1,3,-4,5,2]=>147
[1,3,-4,5,-2]=>63
[1,3,-4,-5,2]=>315
[1,3,-4,-5,-2]=>105
[1,-3,4,5,2]=>114
[1,-3,4,5,-2]=>45
[1,-3,4,-5,2]=>329
[1,-3,4,-5,-2]=>105
[1,-3,-4,5,2]=>364
[1,-3,-4,5,-2]=>126
[1,-3,-4,-5,2]=>490
[1,-3,-4,-5,-2]=>140
[-1,3,4,5,2]=>4
[-1,3,4,5,-2]=>1
[-1,3,4,-5,2]=>15
[-1,3,4,-5,-2]=>3
[-1,3,-4,5,2]=>33
[-1,3,-4,5,-2]=>7
[-1,3,-4,-5,2]=>60
[-1,3,-4,-5,-2]=>10
[-1,-3,4,5,2]=>16
[-1,-3,4,5,-2]=>3
[-1,-3,4,-5,2]=>39
[-1,-3,4,-5,-2]=>6
[-1,-3,-4,5,2]=>30
[-1,-3,-4,5,-2]=>5
[-1,-3,-4,-5,2]=>35
[-1,-3,-4,-5,-2]=>5
[1,3,5,2,4]=>40
[1,3,5,2,-4]=>95
[1,3,5,-2,4]=>22
[1,3,5,-2,-4]=>29
[1,3,-5,2,4]=>105
[1,3,-5,2,-4]=>182
[1,3,-5,-2,4]=>51
[1,3,-5,-2,-4]=>45
[1,-3,5,2,4]=>210
[1,-3,5,2,-4]=>329
[1,-3,5,-2,4]=>89
[1,-3,5,-2,-4]=>60
[1,-3,-5,2,4]=>369
[1,-3,-5,2,-4]=>445
[1,-3,-5,-2,4]=>149
[1,-3,-5,-2,-4]=>68
[-1,3,5,2,4]=>20
[-1,3,5,2,-4]=>35
[-1,3,5,-2,4]=>3
[-1,3,5,-2,-4]=>3
[-1,3,-5,2,4]=>45
[-1,3,-5,2,-4]=>57
[-1,3,-5,-2,4]=>6
[-1,3,-5,-2,-4]=>4
[-1,-3,5,2,4]=>35
[-1,-3,5,2,-4]=>39
[-1,-3,5,-2,4]=>4
[-1,-3,5,-2,-4]=>2
[-1,-3,-5,2,4]=>54
[-1,-3,-5,2,-4]=>46
[-1,-3,-5,-2,4]=>6
[-1,-3,-5,-2,-4]=>2
[1,3,5,4,2]=>45
[1,3,5,4,-2]=>24
[1,3,5,-4,2]=>75
[1,3,5,-4,-2]=>23
[1,3,-5,4,2]=>126
[1,3,-5,4,-2]=>63
[1,3,-5,-4,2]=>133
[1,3,-5,-4,-2]=>35
[1,-3,5,4,2]=>329
[1,-3,5,4,-2]=>142
[1,-3,5,-4,2]=>275
[1,-3,5,-4,-2]=>66
[1,-3,-5,4,2]=>641
[1,-3,-5,4,-2]=>260
[1,-3,-5,-4,2]=>341
[1,-3,-5,-4,-2]=>72
[-1,3,5,4,2]=>15
[-1,3,5,4,-2]=>4
[-1,3,5,-4,2]=>20
[-1,3,5,-4,-2]=>3
[-1,3,-5,4,2]=>36
[-1,3,-5,4,-2]=>9
[-1,3,-5,-4,2]=>31
[-1,3,-5,-4,-2]=>4
[-1,-3,5,4,2]=>39
[-1,-3,5,4,-2]=>8
[-1,-3,5,-4,2]=>26
[-1,-3,5,-4,-2]=>3
[-1,-3,-5,4,2]=>67
[-1,-3,-5,4,-2]=>13
[-1,-3,-5,-4,2]=>29
[-1,-3,-5,-4,-2]=>3
[1,4,2,3,5]=>15
[1,4,2,3,-5]=>75
[1,4,2,-3,5]=>69
[1,4,2,-3,-5]=>218
[1,4,-2,3,5]=>26
[1,4,-2,3,-5]=>96
[1,4,-2,-3,5]=>21
[1,4,-2,-3,-5]=>51
[1,-4,2,3,5]=>56
[1,-4,2,3,-5]=>168
[1,-4,2,-3,5]=>166
[1,-4,2,-3,-5]=>270
[1,-4,-2,3,5]=>75
[1,-4,-2,3,-5]=>151
[1,-4,-2,-3,5]=>37
[1,-4,-2,-3,-5]=>44
[-1,4,2,3,5]=>10
[-1,4,2,3,-5]=>40
[-1,4,2,-3,5]=>19
[-1,4,2,-3,-5]=>49
[-1,4,-2,3,5]=>3
[-1,4,-2,3,-5]=>9
[-1,4,-2,-3,5]=>1
[-1,4,-2,-3,-5]=>2
[-1,-4,2,3,5]=>21
[-1,-4,2,3,-5]=>49
[-1,-4,2,-3,5]=>26
[-1,-4,2,-3,-5]=>34
[-1,-4,-2,3,5]=>5
[-1,-4,-2,3,-5]=>8
[-1,-4,-2,-3,5]=>1
[-1,-4,-2,-3,-5]=>1
[1,4,2,5,3]=>40
[1,4,2,5,-3]=>45
[1,4,2,-5,3]=>155
[1,4,2,-5,-3]=>132
[1,4,-2,5,3]=>35
[1,4,-2,5,-3]=>19
[1,4,-2,-5,3]=>109
[1,4,-2,-5,-3]=>45
[1,-4,2,5,3]=>168
[1,-4,2,5,-3]=>156
[1,-4,2,-5,3]=>324
[1,-4,2,-5,-3]=>220
[1,-4,-2,5,3]=>151
[1,-4,-2,5,-3]=>64
[1,-4,-2,-5,3]=>215
[1,-4,-2,-5,-3]=>72
[-1,4,2,5,3]=>20
[-1,4,2,5,-3]=>15
[-1,4,2,-5,3]=>65
[-1,4,2,-5,-3]=>37
[-1,4,-2,5,3]=>3
[-1,4,-2,5,-3]=>1
[-1,4,-2,-5,3]=>8
[-1,4,-2,-5,-3]=>2
[-1,-4,2,5,3]=>49
[-1,-4,2,5,-3]=>30
[-1,-4,2,-5,3]=>79
[-1,-4,2,-5,-3]=>36
[-1,-4,-2,5,3]=>8
[-1,-4,-2,5,-3]=>2
[-1,-4,-2,-5,3]=>10
[-1,-4,-2,-5,-3]=>2
[1,4,3,2,5]=>40
[1,4,3,2,-5]=>200
[1,4,3,-2,5]=>29
[1,4,3,-2,-5]=>106
[1,4,-3,2,5]=>70
[1,4,-3,2,-5]=>228
[1,4,-3,-2,5]=>16
[1,4,-3,-2,-5]=>38
[1,-4,3,2,5]=>196
[1,-4,3,2,-5]=>576
[1,-4,3,-2,5]=>114
[1,-4,3,-2,-5]=>218
[1,-4,-3,2,5]=>121
[1,-4,-3,2,-5]=>213
[1,-4,-3,-2,5]=>26
[1,-4,-3,-2,-5]=>30
[-1,4,3,2,5]=>20
[-1,4,3,2,-5]=>80
[-1,4,3,-2,5]=>4
[-1,4,3,-2,-5]=>12
[-1,4,-3,2,5]=>16
[-1,4,-3,2,-5]=>42
[-1,4,-3,-2,5]=>1
[-1,4,-3,-2,-5]=>2
[-1,-4,3,2,5]=>56
[-1,-4,3,2,-5]=>128
[-1,-4,3,-2,5]=>9
[-1,-4,3,-2,-5]=>14
[-1,-4,-3,2,5]=>16
[-1,-4,-3,2,-5]=>22
[-1,-4,-3,-2,5]=>1
[-1,-4,-3,-2,-5]=>1
[1,4,3,5,2]=>45
[1,4,3,5,-2]=>24
[1,4,3,-5,2]=>201
[1,4,3,-5,-2]=>86
[1,4,-3,5,2]=>79
[1,4,-3,5,-2]=>26
[1,4,-3,-5,2]=>220
[1,4,-3,-5,-2]=>60
[1,-4,3,5,2]=>252
[1,-4,3,5,-2]=>124
[1,-4,3,-5,2]=>596
[1,-4,3,-5,-2]=>220
[1,-4,-3,5,2]=>213
[1,-4,-3,5,-2]=>62
[1,-4,-3,-5,2]=>275
[1,-4,-3,-5,-2]=>68
[-1,4,3,5,2]=>15
[-1,4,3,5,-2]=>4
[-1,4,3,-5,2]=>56
[-1,4,3,-5,-2]=>12
[-1,4,-3,5,2]=>13
[-1,4,-3,5,-2]=>2
[-1,4,-3,-5,2]=>31
[-1,4,-3,-5,-2]=>4
[-1,-4,3,5,2]=>49
[-1,-4,3,5,-2]=>12
[-1,-4,3,-5,2]=>97
[-1,-4,3,-5,-2]=>18
[-1,-4,-3,5,2]=>22
[-1,-4,-3,5,-2]=>3
[-1,-4,-3,-5,2]=>25
[-1,-4,-3,-5,-2]=>3
[1,4,5,2,3]=>50
[1,4,5,2,-3]=>75
[1,4,5,-2,3]=>29
[1,4,5,-2,-3]=>15
[1,4,-5,2,3]=>175
[1,4,-5,2,-3]=>210
[1,4,-5,-2,3]=>89
[1,4,-5,-2,-3]=>35
[1,-4,5,2,3]=>324
[1,-4,5,2,-3]=>386
[1,-4,5,-2,3]=>218
[1,-4,5,-2,-3]=>76
[1,-4,-5,2,3]=>490
[1,-4,-5,2,-3]=>490
[1,-4,-5,-2,3]=>294
[1,-4,-5,-2,-3]=>84
[-1,4,5,2,3]=>20
[-1,4,5,2,-3]=>20
[-1,4,5,-2,3]=>3
[-1,4,5,-2,-3]=>1
[-1,4,-5,2,3]=>60
[-1,4,-5,2,-3]=>48
[-1,4,-5,-2,3]=>8
[-1,4,-5,-2,-3]=>2
[-1,-4,5,2,3]=>79
[-1,-4,5,2,-3]=>62
[-1,-4,5,-2,3]=>14
[-1,-4,5,-2,-3]=>3
[-1,-4,-5,2,3]=>105
[-1,-4,-5,2,-3]=>70
[-1,-4,-5,-2,3]=>17
[-1,-4,-5,-2,-3]=>3
[1,4,5,3,2]=>75
[1,4,5,3,-2]=>45
[1,4,5,-3,2]=>50
[1,4,5,-3,-2]=>11
[1,4,-5,3,2]=>280
[1,4,-5,3,-2]=>149
[1,4,-5,-3,2]=>131
[1,4,-5,-3,-2]=>25
[1,-4,5,3,2]=>596
[1,-4,5,3,-2]=>334
[1,-4,5,-3,2]=>270
[1,-4,5,-3,-2]=>52
[1,-4,-5,3,2]=>980
[1,-4,-5,3,-2]=>490
[1,-4,-5,-3,2]=>322
[1,-4,-5,-3,-2]=>56
[-1,4,5,3,2]=>20
[-1,4,5,3,-2]=>6
[-1,4,5,-3,2]=>10
[-1,4,5,-3,-2]=>1
[-1,4,-5,3,2]=>64
[-1,4,-5,3,-2]=>17
[-1,4,-5,-3,2]=>23
[-1,4,-5,-3,-2]=>2
[-1,-4,5,3,2]=>97
[-1,-4,5,3,-2]=>27
[-1,-4,5,-3,2]=>34
[-1,-4,5,-3,-2]=>3
[-1,-4,-5,3,2]=>140
[-1,-4,-5,3,-2]=>35
[-1,-4,-5,-3,2]=>37
[-1,-4,-5,-3,-2]=>3
[1,5,2,3,4]=>35
[1,5,2,3,-4]=>105
[1,5,2,-3,4]=>168
[1,5,2,-3,-4]=>210
[1,5,-2,3,4]=>61
[1,5,-2,3,-4]=>109
[1,5,-2,-3,4]=>51
[1,5,-2,-3,-4]=>35
[1,-5,2,3,4]=>70
[1,-5,2,3,-4]=>168
[1,-5,2,-3,4]=>308
[1,-5,2,-3,-4]=>280
[1,-5,-2,3,4]=>115
[1,-5,-2,3,-4]=>155
[1,-5,-2,-3,4]=>86
[1,-5,-2,-3,-4]=>40
[-1,5,2,3,4]=>20
[-1,5,2,3,-4]=>45
[-1,5,2,-3,4]=>39
[-1,5,2,-3,-4]=>36
[-1,5,-2,3,4]=>6
[-1,5,-2,3,-4]=>8
[-1,5,-2,-3,4]=>2
[-1,5,-2,-3,-4]=>1
[-1,-5,2,3,4]=>35
[-1,-5,2,3,-4]=>63
[-1,-5,2,-3,4]=>63
[-1,-5,2,-3,-4]=>42
[-1,-5,-2,3,4]=>10
[-1,-5,-2,3,-4]=>10
[-1,-5,-2,-3,4]=>3
[-1,-5,-2,-3,-4]=>1
[1,5,2,4,3]=>105
[1,5,2,4,-3]=>126
[1,5,2,-4,3]=>175
[1,5,2,-4,-3]=>112
[1,5,-2,4,3]=>109
[1,5,-2,4,-3]=>66
[1,5,-2,-4,3]=>100
[1,5,-2,-4,-3]=>29
[1,-5,2,4,3]=>224
[1,-5,2,4,-3]=>252
[1,-5,2,-4,3]=>252
[1,-5,2,-4,-3]=>140
[1,-5,-2,4,3]=>230
[1,-5,-2,4,-3]=>125
[1,-5,-2,-4,3]=>129
[1,-5,-2,-4,-3]=>32
[-1,5,2,4,3]=>45
[-1,5,2,4,-3]=>36
[-1,5,2,-4,3]=>60
[-1,5,2,-4,-3]=>25
[-1,5,-2,4,3]=>8
[-1,5,-2,4,-3]=>3
[-1,5,-2,-4,3]=>6
[-1,5,-2,-4,-3]=>1
[-1,-5,2,4,3]=>84
[-1,-5,2,4,-3]=>63
[-1,-5,2,-4,3]=>77
[-1,-5,2,-4,-3]=>28
[-1,-5,-2,4,3]=>15
[-1,-5,-2,4,-3]=>5
[-1,-5,-2,-4,3]=>7
[-1,-5,-2,-4,-3]=>1
[1,5,3,2,4]=>105
[1,5,3,2,-4]=>301
[1,5,3,-2,4]=>77
[1,5,3,-2,-4]=>124
[1,5,-3,2,4]=>149
[1,5,-3,2,-4]=>220
[1,5,-3,-2,4]=>38
[1,5,-3,-2,-4]=>25
[1,-5,3,2,4]=>224
[1,-5,3,2,-4]=>504
[1,-5,3,-2,4]=>156
[1,-5,3,-2,-4]=>180
[1,-5,-3,2,4]=>254
[1,-5,-3,2,-4]=>290
[1,-5,-3,-2,4]=>63
[1,-5,-3,-2,-4]=>28
[-1,5,3,2,4]=>45
[-1,5,3,2,-4]=>96
[-1,5,3,-2,4]=>9
[-1,5,3,-2,-4]=>11
[-1,5,-3,2,4]=>29
[-1,5,-3,2,-4]=>31
[-1,5,-3,-2,4]=>2
[-1,5,-3,-2,-4]=>1
[-1,-5,3,2,4]=>84
[-1,-5,3,2,-4]=>140
[-1,-5,3,-2,4]=>16
[-1,-5,3,-2,-4]=>14
[-1,-5,-3,2,4]=>44
[-1,-5,-3,2,-4]=>36
[-1,-5,-3,-2,4]=>3
[-1,-5,-3,-2,-4]=>1
[1,5,3,4,2]=>126
[1,5,3,4,-2]=>70
[1,5,3,-4,2]=>280
[1,5,3,-4,-2]=>98
[1,5,-3,4,2]=>220
[1,5,-3,4,-2]=>76
[1,5,-3,-4,2]=>175
[1,5,-3,-4,-2]=>37
[1,-5,3,4,2]=>280
[1,-5,3,4,-2]=>152
[1,-5,3,-4,2]=>448
[1,-5,3,-4,-2]=>140
[1,-5,-3,4,2]=>411
[1,-5,-3,4,-2]=>135
[1,-5,-3,-4,2]=>212
[1,-5,-3,-4,-2]=>40
[-1,5,3,4,2]=>36
[-1,5,3,4,-2]=>10
[-1,5,3,-4,2]=>64
[-1,5,3,-4,-2]=>11
[-1,5,-3,4,2]=>31
[-1,5,-3,4,-2]=>5
[-1,5,-3,-4,2]=>20
[-1,5,-3,-4,-2]=>2
[-1,-5,3,4,2]=>70
[-1,-5,3,4,-2]=>19
[-1,-5,3,-4,2]=>91
[-1,-5,3,-4,-2]=>14
[-1,-5,-3,4,2]=>52
[-1,-5,-3,4,-2]=>8
[-1,-5,-3,-4,2]=>22
[-1,-5,-3,-4,-2]=>2
[1,5,4,2,3]=>175
[1,5,4,2,-3]=>280
[1,5,4,-2,3]=>124
[1,5,4,-2,-3]=>70
[1,5,-4,2,3]=>175
[1,5,-4,2,-3]=>166
[1,5,-4,-2,3]=>80
[1,5,-4,-2,-3]=>22
[1,-5,4,2,3]=>420
[1,-5,4,2,-3]=>604
[1,-5,4,-2,3]=>294
[1,-5,4,-2,-3]=>140
[1,-5,-4,2,3]=>236
[1,-5,-4,2,-3]=>200
[1,-5,-4,-2,3]=>102
[1,-5,-4,-2,-3]=>24
[-1,5,4,2,3]=>60
[-1,5,4,2,-3]=>64
[-1,5,4,-2,3]=>11
[-1,5,4,-2,-3]=>4
[-1,5,-4,2,3]=>50
[-1,5,-4,2,-3]=>31
[-1,5,-4,-2,3]=>6
[-1,5,-4,-2,-3]=>1
[-1,-5,4,2,3]=>126
[-1,-5,4,2,-3]=>121
[-1,-5,4,-2,3]=>23
[-1,-5,4,-2,-3]=>7
[-1,-5,-4,2,3]=>61
[-1,-5,-4,2,-3]=>34
[-1,-5,-4,-2,3]=>7
[-1,-5,-4,-2,-3]=>1
[1,5,4,3,2]=>280
[1,5,4,3,-2]=>175
[1,5,4,-3,2]=>210
[1,5,4,-3,-2]=>51
[1,5,-4,3,2]=>315
[1,5,-4,3,-2]=>149
[1,5,-4,-3,2]=>95
[1,5,-4,-3,-2]=>15
[1,-5,4,3,2]=>700
[1,-5,4,3,-2]=>420
[1,-5,4,-3,2]=>446
[1,-5,4,-3,-2]=>100
[1,-5,-4,3,2]=>454
[1,-5,-4,3,-2]=>200
[1,-5,-4,-3,2]=>110
[1,-5,-4,-3,-2]=>16
[-1,5,4,3,2]=>64
[-1,5,4,3,-2]=>20
[-1,5,4,-3,2]=>36
[-1,5,4,-3,-2]=>4
[-1,5,-4,3,2]=>60
[-1,5,-4,3,-2]=>14
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Description
The number of facets of a certain subword complex associated with the signed permutation.
Let $Q=[1,\dots,n,1,\dots,n,\dots,1,\dots,n]$ be the word of length $n^2$, and let $\pi$ be a signed permutation. Then this statistic yields the number of facets of the subword complex $\Delta(Q, \pi)$.
Let $Q=[1,\dots,n,1,\dots,n,\dots,1,\dots,n]$ be the word of length $n^2$, and let $\pi$ be a signed permutation. Then this statistic yields the number of facets of the subword complex $\Delta(Q, \pi)$.
Code
def statistic(pi):
n = len(list(pi))
S = SignedPermutations(n)
Q = S.w0.coxeter_sorting_word(S.coxeter_element())
return len(SubwordComplex(Q, pi).facets())
Created
Feb 05, 2022 at 17:47 by Martin Rubey
Updated
Feb 05, 2022 at 17:47 by Martin Rubey
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