Identifier
Values
=>
Cc0007;cc-rep
[[1,2]]=>4
[[1],[2]]=>0
[[1,2,3]]=>9
[[1,3],[2]]=>0
[[1,2],[3]]=>4
[[1],[2],[3]]=>1
[[1,2,3,4]]=>16
[[1,3,4],[2]]=>0
[[1,2,4],[3]]=>6
[[1,2,3],[4]]=>10
[[1,3],[2,4]]=>0
[[1,2],[3,4]]=>4
[[1,4],[2],[3]]=>2
[[1,3],[2],[4]]=>0
[[1,2],[3],[4]]=>6
[[1],[2],[3],[4]]=>0
[[1,2,3,4,5]]=>25
[[1,3,4,5],[2]]=>0
[[1,2,4,5],[3]]=>8
[[1,2,3,5],[4]]=>14
[[1,2,3,4],[5]]=>18
[[1,3,5],[2,4]]=>0
[[1,2,5],[3,4]]=>5
[[1,3,4],[2,5]]=>0
[[1,2,4],[3,5]]=>7
[[1,2,3],[4,5]]=>11
[[1,4,5],[2],[3]]=>3
[[1,3,5],[2],[4]]=>0
[[1,2,5],[3],[4]]=>9
[[1,3,4],[2],[5]]=>0
[[1,2,4],[3],[5]]=>7
[[1,2,3],[4],[5]]=>13
[[1,4],[2,5],[3]]=>3
[[1,3],[2,5],[4]]=>0
[[1,2],[3,5],[4]]=>7
[[1,3],[2,4],[5]]=>0
[[1,2],[3,4],[5]]=>5
[[1,5],[2],[3],[4]]=>0
[[1,4],[2],[3],[5]]=>2
[[1,3],[2],[4],[5]]=>0
[[1,2],[3],[4],[5]]=>6
[[1],[2],[3],[4],[5]]=>1
[[1,2,3,4,5,6]]=>36
[[1,3,4,5,6],[2]]=>0
[[1,2,4,5,6],[3]]=>10
[[1,2,3,5,6],[4]]=>18
[[1,2,3,4,6],[5]]=>24
[[1,2,3,4,5],[6]]=>28
[[1,3,5,6],[2,4]]=>0
[[1,2,5,6],[3,4]]=>6
[[1,3,4,6],[2,5]]=>0
[[1,2,4,6],[3,5]]=>9
[[1,2,3,6],[4,5]]=>14
[[1,3,4,5],[2,6]]=>0
[[1,2,4,5],[3,6]]=>9
[[1,2,3,5],[4,6]]=>16
[[1,2,3,4],[5,6]]=>20
[[1,4,5,6],[2],[3]]=>4
[[1,3,5,6],[2],[4]]=>0
[[1,2,5,6],[3],[4]]=>12
[[1,3,4,6],[2],[5]]=>0
[[1,2,4,6],[3],[5]]=>9
[[1,2,3,6],[4],[5]]=>18
[[1,3,4,5],[2],[6]]=>0
[[1,2,4,5],[3],[6]]=>9
[[1,2,3,5],[4],[6]]=>16
[[1,2,3,4],[5],[6]]=>22
[[1,3,5],[2,4,6]]=>0
[[1,2,5],[3,4,6]]=>7
[[1,3,4],[2,5,6]]=>0
[[1,2,4],[3,5,6]]=>7
[[1,2,3],[4,5,6]]=>12
[[1,4,6],[2,5],[3]]=>4
[[1,3,6],[2,5],[4]]=>0
[[1,2,6],[3,5],[4]]=>9
[[1,3,6],[2,4],[5]]=>0
[[1,2,6],[3,4],[5]]=>6
[[1,4,5],[2,6],[3]]=>4
[[1,3,5],[2,6],[4]]=>0
[[1,2,5],[3,6],[4]]=>11
[[1,3,4],[2,6],[5]]=>0
[[1,2,4],[3,6],[5]]=>8
[[1,2,3],[4,6],[5]]=>15
[[1,3,5],[2,4],[6]]=>0
[[1,2,5],[3,4],[6]]=>6
[[1,3,4],[2,5],[6]]=>0
[[1,2,4],[3,5],[6]]=>8
[[1,2,3],[4,5],[6]]=>13
[[1,5,6],[2],[3],[4]]=>0
[[1,4,6],[2],[3],[5]]=>3
[[1,3,6],[2],[4],[5]]=>0
[[1,2,6],[3],[4],[5]]=>8
[[1,4,5],[2],[3],[6]]=>3
[[1,3,5],[2],[4],[6]]=>0
[[1,2,5],[3],[4],[6]]=>10
[[1,3,4],[2],[5],[6]]=>0
[[1,2,4],[3],[5],[6]]=>8
[[1,2,3],[4],[5],[6]]=>14
[[1,4],[2,5],[3,6]]=>5
[[1,3],[2,5],[4,6]]=>0
[[1,2],[3,5],[4,6]]=>8
[[1,3],[2,4],[5,6]]=>0
[[1,2],[3,4],[5,6]]=>5
[[1,5],[2,6],[3],[4]]=>0
[[1,4],[2,6],[3],[5]]=>3
[[1,3],[2,6],[4],[5]]=>0
[[1,2],[3,6],[4],[5]]=>6
[[1,4],[2,5],[3],[6]]=>3
[[1,3],[2,5],[4],[6]]=>0
[[1,2],[3,5],[4],[6]]=>8
[[1,3],[2,4],[5],[6]]=>0
[[1,2],[3,4],[5],[6]]=>6
[[1,6],[2],[3],[4],[5]]=>2
[[1,5],[2],[3],[4],[6]]=>0
[[1,4],[2],[3],[5],[6]]=>2
[[1,3],[2],[4],[5],[6]]=>0
[[1,2],[3],[4],[5],[6]]=>8
[[1],[2],[3],[4],[5],[6]]=>0
[[1,2,3,4,5,6,7]]=>49
[[1,3,4,5,6,7],[2]]=>0
[[1,2,4,5,6,7],[3]]=>12
[[1,2,3,5,6,7],[4]]=>22
[[1,2,3,4,6,7],[5]]=>30
[[1,2,3,4,5,7],[6]]=>36
[[1,2,3,4,5,6],[7]]=>40
[[1,3,5,6,7],[2,4]]=>0
[[1,2,5,6,7],[3,4]]=>7
[[1,3,4,6,7],[2,5]]=>0
[[1,2,4,6,7],[3,5]]=>11
[[1,2,3,6,7],[4,5]]=>17
[[1,3,4,5,7],[2,6]]=>0
[[1,2,4,5,7],[3,6]]=>11
[[1,2,3,5,7],[4,6]]=>20
[[1,2,3,4,7],[5,6]]=>25
[[1,3,4,5,6],[2,7]]=>0
[[1,2,4,5,6],[3,7]]=>11
[[1,2,3,5,6],[4,7]]=>20
[[1,2,3,4,6],[5,7]]=>27
[[1,2,3,4,5],[6,7]]=>31
[[1,4,5,6,7],[2],[3]]=>5
[[1,3,5,6,7],[2],[4]]=>0
[[1,2,5,6,7],[3],[4]]=>15
[[1,3,4,6,7],[2],[5]]=>0
[[1,2,4,6,7],[3],[5]]=>11
[[1,2,3,6,7],[4],[5]]=>23
[[1,3,4,5,7],[2],[6]]=>0
[[1,2,4,5,7],[3],[6]]=>11
[[1,2,3,5,7],[4],[6]]=>20
[[1,2,3,4,7],[5],[6]]=>29
[[1,3,4,5,6],[2],[7]]=>0
[[1,2,4,5,6],[3],[7]]=>11
[[1,2,3,5,6],[4],[7]]=>20
[[1,2,3,4,6],[5],[7]]=>27
[[1,2,3,4,5],[6],[7]]=>33
[[1,3,5,7],[2,4,6]]=>0
[[1,2,5,7],[3,4,6]]=>8
[[1,3,4,7],[2,5,6]]=>0
[[1,2,4,7],[3,5,6]]=>8
[[1,2,3,7],[4,5,6]]=>14
[[1,3,5,6],[2,4,7]]=>0
[[1,2,5,6],[3,4,7]]=>8
[[1,3,4,6],[2,5,7]]=>0
[[1,2,4,6],[3,5,7]]=>10
[[1,2,3,6],[4,5,7]]=>17
[[1,3,4,5],[2,6,7]]=>0
[[1,2,4,5],[3,6,7]]=>10
[[1,2,3,5],[4,6,7]]=>17
[[1,2,3,4],[5,6,7]]=>22
[[1,4,6,7],[2,5],[3]]=>5
[[1,3,6,7],[2,5],[4]]=>0
[[1,2,6,7],[3,5],[4]]=>11
[[1,3,6,7],[2,4],[5]]=>0
[[1,2,6,7],[3,4],[5]]=>7
[[1,4,5,7],[2,6],[3]]=>5
[[1,3,5,7],[2,6],[4]]=>0
[[1,2,5,7],[3,6],[4]]=>14
[[1,3,4,7],[2,6],[5]]=>0
[[1,2,4,7],[3,6],[5]]=>10
[[1,2,3,7],[4,6],[5]]=>19
[[1,3,5,7],[2,4],[6]]=>0
[[1,2,5,7],[3,4],[6]]=>7
[[1,3,4,7],[2,5],[6]]=>0
[[1,2,4,7],[3,5],[6]]=>10
[[1,2,3,7],[4,5],[6]]=>16
[[1,4,5,6],[2,7],[3]]=>5
[[1,3,5,6],[2,7],[4]]=>0
[[1,2,5,6],[3,7],[4]]=>14
[[1,3,4,6],[2,7],[5]]=>0
[[1,2,4,6],[3,7],[5]]=>10
[[1,2,3,6],[4,7],[5]]=>21
[[1,3,4,5],[2,7],[6]]=>0
[[1,2,4,5],[3,7],[6]]=>10
[[1,2,3,5],[4,7],[6]]=>18
[[1,2,3,4],[5,7],[6]]=>25
[[1,3,5,6],[2,4],[7]]=>0
[[1,2,5,6],[3,4],[7]]=>7
[[1,3,4,6],[2,5],[7]]=>0
[[1,2,4,6],[3,5],[7]]=>10
[[1,2,3,6],[4,5],[7]]=>16
[[1,3,4,5],[2,6],[7]]=>0
[[1,2,4,5],[3,6],[7]]=>10
[[1,2,3,5],[4,6],[7]]=>18
[[1,2,3,4],[5,6],[7]]=>23
[[1,5,6,7],[2],[3],[4]]=>0
[[1,4,6,7],[2],[3],[5]]=>4
[[1,3,6,7],[2],[4],[5]]=>0
[[1,2,6,7],[3],[4],[5]]=>10
[[1,4,5,7],[2],[3],[6]]=>4
[[1,3,5,7],[2],[4],[6]]=>0
[[1,2,5,7],[3],[4],[6]]=>13
[[1,3,4,7],[2],[5],[6]]=>0
[[1,2,4,7],[3],[5],[6]]=>10
[[1,2,3,7],[4],[5],[6]]=>18
[[1,4,5,6],[2],[3],[7]]=>4
[[1,3,5,6],[2],[4],[7]]=>0
[[1,2,5,6],[3],[4],[7]]=>13
[[1,3,4,6],[2],[5],[7]]=>0
[[1,2,4,6],[3],[5],[7]]=>10
[[1,2,3,6],[4],[5],[7]]=>20
[[1,3,4,5],[2],[6],[7]]=>0
[[1,2,4,5],[3],[6],[7]]=>10
[[1,2,3,5],[4],[6],[7]]=>18
[[1,2,3,4],[5],[6],[7]]=>24
[[1,4,6],[2,5,7],[3]]=>5
[[1,3,6],[2,5,7],[4]]=>0
[[1,2,6],[3,5,7],[4]]=>12
[[1,3,6],[2,4,7],[5]]=>0
[[1,2,6],[3,4,7],[5]]=>8
[[1,4,5],[2,6,7],[3]]=>5
[[1,3,5],[2,6,7],[4]]=>0
[[1,2,5],[3,6,7],[4]]=>12
[[1,3,4],[2,6,7],[5]]=>0
[[1,2,4],[3,6,7],[5]]=>8
[[1,2,3],[4,6,7],[5]]=>17
[[1,3,5],[2,4,7],[6]]=>0
[[1,2,5],[3,4,7],[6]]=>8
[[1,3,4],[2,5,7],[6]]=>0
[[1,2,4],[3,5,7],[6]]=>8
[[1,2,3],[4,5,7],[6]]=>14
[[1,3,5],[2,4,6],[7]]=>0
[[1,2,5],[3,4,6],[7]]=>8
[[1,3,4],[2,5,6],[7]]=>0
[[1,2,4],[3,5,6],[7]]=>8
[[1,2,3],[4,5,6],[7]]=>14
[[1,4,7],[2,5],[3,6]]=>6
[[1,3,7],[2,5],[4,6]]=>0
[[1,2,7],[3,5],[4,6]]=>10
[[1,3,7],[2,4],[5,6]]=>0
[[1,2,7],[3,4],[5,6]]=>6
[[1,4,6],[2,5],[3,7]]=>6
[[1,3,6],[2,5],[4,7]]=>0
[[1,2,6],[3,5],[4,7]]=>10
[[1,3,6],[2,4],[5,7]]=>0
[[1,2,6],[3,4],[5,7]]=>6
[[1,4,5],[2,6],[3,7]]=>6
[[1,3,5],[2,6],[4,7]]=>0
[[1,2,5],[3,6],[4,7]]=>14
[[1,3,4],[2,6],[5,7]]=>0
[[1,2,4],[3,6],[5,7]]=>9
[[1,2,3],[4,6],[5,7]]=>17
[[1,3,5],[2,4],[6,7]]=>0
[[1,2,5],[3,4],[6,7]]=>6
[[1,3,4],[2,5],[6,7]]=>0
[[1,2,4],[3,5],[6,7]]=>9
[[1,2,3],[4,5],[6,7]]=>14
[[1,5,7],[2,6],[3],[4]]=>0
[[1,4,7],[2,6],[3],[5]]=>4
[[1,3,7],[2,6],[4],[5]]=>0
[[1,2,7],[3,6],[4],[5]]=>7
[[1,4,7],[2,5],[3],[6]]=>4
[[1,3,7],[2,5],[4],[6]]=>0
[[1,2,7],[3,5],[4],[6]]=>10
[[1,3,7],[2,4],[5],[6]]=>0
[[1,2,7],[3,4],[5],[6]]=>7
[[1,5,6],[2,7],[3],[4]]=>0
[[1,4,6],[2,7],[3],[5]]=>4
[[1,3,6],[2,7],[4],[5]]=>0
[[1,2,6],[3,7],[4],[5]]=>9
[[1,4,5],[2,7],[3],[6]]=>4
[[1,3,5],[2,7],[4],[6]]=>0
[[1,2,5],[3,7],[4],[6]]=>12
[[1,3,4],[2,7],[5],[6]]=>0
[[1,2,4],[3,7],[5],[6]]=>9
[[1,2,3],[4,7],[5],[6]]=>15
[[1,4,6],[2,5],[3],[7]]=>4
[[1,3,6],[2,5],[4],[7]]=>0
[[1,2,6],[3,5],[4],[7]]=>10
[[1,3,6],[2,4],[5],[7]]=>0
[[1,2,6],[3,4],[5],[7]]=>7
[[1,4,5],[2,6],[3],[7]]=>4
[[1,3,5],[2,6],[4],[7]]=>0
[[1,2,5],[3,6],[4],[7]]=>12
[[1,3,4],[2,6],[5],[7]]=>0
[[1,2,4],[3,6],[5],[7]]=>9
[[1,2,3],[4,6],[5],[7]]=>17
[[1,3,5],[2,4],[6],[7]]=>0
[[1,2,5],[3,4],[6],[7]]=>7
[[1,3,4],[2,5],[6],[7]]=>0
[[1,2,4],[3,5],[6],[7]]=>9
[[1,2,3],[4,5],[6],[7]]=>15
[[1,6,7],[2],[3],[4],[5]]=>3
[[1,5,7],[2],[3],[4],[6]]=>0
[[1,4,7],[2],[3],[5],[6]]=>3
[[1,3,7],[2],[4],[5],[6]]=>0
[[1,2,7],[3],[4],[5],[6]]=>11
[[1,5,6],[2],[3],[4],[7]]=>0
[[1,4,6],[2],[3],[5],[7]]=>3
[[1,3,6],[2],[4],[5],[7]]=>0
[[1,2,6],[3],[4],[5],[7]]=>9
[[1,4,5],[2],[3],[6],[7]]=>3
[[1,3,5],[2],[4],[6],[7]]=>0
[[1,2,5],[3],[4],[6],[7]]=>11
[[1,3,4],[2],[5],[6],[7]]=>0
[[1,2,4],[3],[5],[6],[7]]=>9
[[1,2,3],[4],[5],[6],[7]]=>17
[[1,5],[2,6],[3,7],[4]]=>0
[[1,4],[2,6],[3,7],[5]]=>4
[[1,3],[2,6],[4,7],[5]]=>0
[[1,2],[3,6],[4,7],[5]]=>6
[[1,4],[2,5],[3,7],[6]]=>4
[[1,3],[2,5],[4,7],[6]]=>0
[[1,2],[3,5],[4,7],[6]]=>9
[[1,3],[2,4],[5,7],[6]]=>0
[[1,2],[3,4],[5,7],[6]]=>6
[[1,4],[2,5],[3,6],[7]]=>6
[[1,3],[2,5],[4,6],[7]]=>0
[[1,2],[3,5],[4,6],[7]]=>9
[[1,3],[2,4],[5,6],[7]]=>0
[[1,2],[3,4],[5,6],[7]]=>6
[[1,6],[2,7],[3],[4],[5]]=>3
[[1,5],[2,7],[3],[4],[6]]=>0
[[1,4],[2,7],[3],[5],[6]]=>3
[[1,3],[2,7],[4],[5],[6]]=>0
[[1,2],[3,7],[4],[5],[6]]=>9
[[1,5],[2,6],[3],[4],[7]]=>0
[[1,4],[2,6],[3],[5],[7]]=>3
[[1,3],[2,6],[4],[5],[7]]=>0
[[1,2],[3,6],[4],[5],[7]]=>7
[[1,4],[2,5],[3],[6],[7]]=>3
[[1,3],[2,5],[4],[6],[7]]=>0
[[1,2],[3,5],[4],[6],[7]]=>9
[[1,3],[2,4],[5],[6],[7]]=>0
[[1,2],[3,4],[5],[6],[7]]=>7
[[1,7],[2],[3],[4],[5],[6]]=>0
[[1,6],[2],[3],[4],[5],[7]]=>2
[[1,5],[2],[3],[4],[6],[7]]=>0
[[1,4],[2],[3],[5],[6],[7]]=>2
[[1,3],[2],[4],[5],[6],[7]]=>0
[[1,2],[3],[4],[5],[6],[7]]=>8
[[1],[2],[3],[4],[5],[6],[7]]=>1
[[1,2,3,4,5,6,7,8]]=>64
[[1,3,4,5,6,7,8],[2]]=>0
[[1,2,4,5,6,7,8],[3]]=>14
[[1,2,3,5,6,7,8],[4]]=>26
[[1,2,3,4,6,7,8],[5]]=>36
[[1,2,3,4,5,7,8],[6]]=>44
[[1,2,3,4,5,6,8],[7]]=>50
[[1,2,3,4,5,6,7],[8]]=>54
[[1,3,5,6,7,8],[2,4]]=>0
[[1,2,5,6,7,8],[3,4]]=>8
[[1,3,4,6,7,8],[2,5]]=>0
[[1,2,4,6,7,8],[3,5]]=>13
[[1,2,3,6,7,8],[4,5]]=>20
[[1,3,4,5,7,8],[2,6]]=>0
[[1,2,4,5,7,8],[3,6]]=>13
[[1,2,3,5,7,8],[4,6]]=>24
[[1,2,3,4,7,8],[5,6]]=>30
[[1,3,4,5,6,8],[2,7]]=>0
[[1,2,4,5,6,8],[3,7]]=>13
[[1,2,3,5,6,8],[4,7]]=>24
[[1,2,3,4,6,8],[5,7]]=>33
[[1,2,3,4,5,8],[6,7]]=>38
[[1,3,4,5,6,7],[2,8]]=>0
[[1,2,4,5,6,7],[3,8]]=>13
[[1,2,3,5,6,7],[4,8]]=>24
[[1,2,3,4,6,7],[5,8]]=>33
[[1,2,3,4,5,7],[6,8]]=>40
[[1,2,3,4,5,6],[7,8]]=>44
[[1,4,5,6,7,8],[2],[3]]=>6
[[1,3,5,6,7,8],[2],[4]]=>0
[[1,2,5,6,7,8],[3],[4]]=>18
[[1,3,4,6,7,8],[2],[5]]=>0
[[1,2,4,6,7,8],[3],[5]]=>13
[[1,2,3,6,7,8],[4],[5]]=>28
[[1,3,4,5,7,8],[2],[6]]=>0
[[1,2,4,5,7,8],[3],[6]]=>13
[[1,2,3,5,7,8],[4],[6]]=>24
[[1,2,3,4,7,8],[5],[6]]=>36
[[1,3,4,5,6,8],[2],[7]]=>0
[[1,2,4,5,6,8],[3],[7]]=>13
[[1,2,3,5,6,8],[4],[7]]=>24
[[1,2,3,4,6,8],[5],[7]]=>33
[[1,2,3,4,5,8],[6],[7]]=>42
[[1,3,4,5,6,7],[2],[8]]=>0
[[1,2,4,5,6,7],[3],[8]]=>13
[[1,2,3,5,6,7],[4],[8]]=>24
[[1,2,3,4,6,7],[5],[8]]=>33
[[1,2,3,4,5,7],[6],[8]]=>40
[[1,2,3,4,5,6],[7],[8]]=>46
[[1,3,5,7,8],[2,4,6]]=>0
[[1,2,5,7,8],[3,4,6]]=>9
[[1,3,4,7,8],[2,5,6]]=>0
[[1,2,4,7,8],[3,5,6]]=>9
[[1,2,3,7,8],[4,5,6]]=>16
[[1,3,5,6,8],[2,4,7]]=>0
[[1,2,5,6,8],[3,4,7]]=>9
[[1,3,4,6,8],[2,5,7]]=>0
[[1,2,4,6,8],[3,5,7]]=>12
[[1,2,3,6,8],[4,5,7]]=>20
[[1,3,4,5,8],[2,6,7]]=>0
[[1,2,4,5,8],[3,6,7]]=>12
[[1,2,3,5,8],[4,6,7]]=>20
[[1,2,3,4,8],[5,6,7]]=>26
[[1,3,5,6,7],[2,4,8]]=>0
[[1,2,5,6,7],[3,4,8]]=>9
[[1,3,4,6,7],[2,5,8]]=>0
[[1,2,4,6,7],[3,5,8]]=>12
[[1,2,3,6,7],[4,5,8]]=>20
[[1,3,4,5,7],[2,6,8]]=>0
[[1,2,4,5,7],[3,6,8]]=>12
[[1,2,3,5,7],[4,6,8]]=>22
[[1,2,3,4,7],[5,6,8]]=>29
[[1,3,4,5,6],[2,7,8]]=>0
[[1,2,4,5,6],[3,7,8]]=>12
[[1,2,3,5,6],[4,7,8]]=>22
[[1,2,3,4,6],[5,7,8]]=>29
[[1,2,3,4,5],[6,7,8]]=>34
[[1,4,6,7,8],[2,5],[3]]=>6
[[1,3,6,7,8],[2,5],[4]]=>0
[[1,2,6,7,8],[3,5],[4]]=>13
[[1,3,6,7,8],[2,4],[5]]=>0
[[1,2,6,7,8],[3,4],[5]]=>8
[[1,4,5,7,8],[2,6],[3]]=>6
[[1,3,5,7,8],[2,6],[4]]=>0
[[1,2,5,7,8],[3,6],[4]]=>17
[[1,3,4,7,8],[2,6],[5]]=>0
[[1,2,4,7,8],[3,6],[5]]=>12
[[1,2,3,7,8],[4,6],[5]]=>23
[[1,3,5,7,8],[2,4],[6]]=>0
[[1,2,5,7,8],[3,4],[6]]=>8
[[1,3,4,7,8],[2,5],[6]]=>0
[[1,2,4,7,8],[3,5],[6]]=>12
[[1,2,3,7,8],[4,5],[6]]=>19
[[1,4,5,6,8],[2,7],[3]]=>6
[[1,3,5,6,8],[2,7],[4]]=>0
[[1,2,5,6,8],[3,7],[4]]=>17
[[1,3,4,6,8],[2,7],[5]]=>0
[[1,2,4,6,8],[3,7],[5]]=>12
[[1,2,3,6,8],[4,7],[5]]=>26
[[1,3,4,5,8],[2,7],[6]]=>0
[[1,2,4,5,8],[3,7],[6]]=>12
[[1,2,3,5,8],[4,7],[6]]=>22
[[1,2,3,4,8],[5,7],[6]]=>31
[[1,3,5,6,8],[2,4],[7]]=>0
[[1,2,5,6,8],[3,4],[7]]=>8
[[1,3,4,6,8],[2,5],[7]]=>0
[[1,2,4,6,8],[3,5],[7]]=>12
[[1,2,3,6,8],[4,5],[7]]=>19
[[1,3,4,5,8],[2,6],[7]]=>0
[[1,2,4,5,8],[3,6],[7]]=>12
[[1,2,3,5,8],[4,6],[7]]=>22
[[1,2,3,4,8],[5,6],[7]]=>28
[[1,4,5,6,7],[2,8],[3]]=>6
[[1,3,5,6,7],[2,8],[4]]=>0
[[1,2,5,6,7],[3,8],[4]]=>17
[[1,3,4,6,7],[2,8],[5]]=>0
[[1,2,4,6,7],[3,8],[5]]=>12
[[1,2,3,6,7],[4,8],[5]]=>26
[[1,3,4,5,7],[2,8],[6]]=>0
[[1,2,4,5,7],[3,8],[6]]=>12
[[1,2,3,5,7],[4,8],[6]]=>22
[[1,2,3,4,7],[5,8],[6]]=>33
[[1,3,4,5,6],[2,8],[7]]=>0
[[1,2,4,5,6],[3,8],[7]]=>12
[[1,2,3,5,6],[4,8],[7]]=>22
[[1,2,3,4,6],[5,8],[7]]=>30
[[1,2,3,4,5],[6,8],[7]]=>37
[[1,3,5,6,7],[2,4],[8]]=>0
[[1,2,5,6,7],[3,4],[8]]=>8
[[1,3,4,6,7],[2,5],[8]]=>0
[[1,2,4,6,7],[3,5],[8]]=>12
[[1,2,3,6,7],[4,5],[8]]=>19
[[1,3,4,5,7],[2,6],[8]]=>0
[[1,2,4,5,7],[3,6],[8]]=>12
[[1,2,3,5,7],[4,6],[8]]=>22
[[1,2,3,4,7],[5,6],[8]]=>28
[[1,3,4,5,6],[2,7],[8]]=>0
[[1,2,4,5,6],[3,7],[8]]=>12
[[1,2,3,5,6],[4,7],[8]]=>22
[[1,2,3,4,6],[5,7],[8]]=>30
[[1,2,3,4,5],[6,7],[8]]=>35
[[1,5,6,7,8],[2],[3],[4]]=>0
[[1,4,6,7,8],[2],[3],[5]]=>5
[[1,3,6,7,8],[2],[4],[5]]=>0
[[1,2,6,7,8],[3],[4],[5]]=>12
[[1,4,5,7,8],[2],[3],[6]]=>5
[[1,3,5,7,8],[2],[4],[6]]=>0
[[1,2,5,7,8],[3],[4],[6]]=>16
[[1,3,4,7,8],[2],[5],[6]]=>0
[[1,2,4,7,8],[3],[5],[6]]=>12
[[1,2,3,7,8],[4],[5],[6]]=>22
[[1,4,5,6,8],[2],[3],[7]]=>5
[[1,3,5,6,8],[2],[4],[7]]=>0
[[1,2,5,6,8],[3],[4],[7]]=>16
[[1,3,4,6,8],[2],[5],[7]]=>0
[[1,2,4,6,8],[3],[5],[7]]=>12
[[1,2,3,6,8],[4],[5],[7]]=>25
[[1,3,4,5,8],[2],[6],[7]]=>0
[[1,2,4,5,8],[3],[6],[7]]=>12
[[1,2,3,5,8],[4],[6],[7]]=>22
[[1,2,3,4,8],[5],[6],[7]]=>30
[[1,4,5,6,7],[2],[3],[8]]=>5
[[1,3,5,6,7],[2],[4],[8]]=>0
[[1,2,5,6,7],[3],[4],[8]]=>16
[[1,3,4,6,7],[2],[5],[8]]=>0
[[1,2,4,6,7],[3],[5],[8]]=>12
[[1,2,3,6,7],[4],[5],[8]]=>25
[[1,3,4,5,7],[2],[6],[8]]=>0
[[1,2,4,5,7],[3],[6],[8]]=>12
[[1,2,3,5,7],[4],[6],[8]]=>22
[[1,2,3,4,7],[5],[6],[8]]=>32
[[1,3,4,5,6],[2],[7],[8]]=>0
[[1,2,4,5,6],[3],[7],[8]]=>12
[[1,2,3,5,6],[4],[7],[8]]=>22
[[1,2,3,4,6],[5],[7],[8]]=>30
[[1,2,3,4,5],[6],[7],[8]]=>36
[[1,3,5,7],[2,4,6,8]]=>0
[[1,2,5,7],[3,4,6,8]]=>10
[[1,3,4,7],[2,5,6,8]]=>0
[[1,2,4,7],[3,5,6,8]]=>10
[[1,2,3,7],[4,5,6,8]]=>18
[[1,3,5,6],[2,4,7,8]]=>0
[[1,2,5,6],[3,4,7,8]]=>10
[[1,3,4,6],[2,5,7,8]]=>0
[[1,2,4,6],[3,5,7,8]]=>10
[[1,2,3,6],[4,5,7,8]]=>18
[[1,3,4,5],[2,6,7,8]]=>0
[[1,2,4,5],[3,6,7,8]]=>10
[[1,2,3,5],[4,6,7,8]]=>18
[[1,2,3,4],[5,6,7,8]]=>24
[[1,4,6,8],[2,5,7],[3]]=>6
[[1,3,6,8],[2,5,7],[4]]=>0
[[1,2,6,8],[3,5,7],[4]]=>14
[[1,3,6,8],[2,4,7],[5]]=>0
[[1,2,6,8],[3,4,7],[5]]=>9
[[1,4,5,8],[2,6,7],[3]]=>6
[[1,3,5,8],[2,6,7],[4]]=>0
[[1,2,5,8],[3,6,7],[4]]=>14
[[1,3,4,8],[2,6,7],[5]]=>0
[[1,2,4,8],[3,6,7],[5]]=>9
[[1,2,3,8],[4,6,7],[5]]=>20
[[1,3,5,8],[2,4,7],[6]]=>0
[[1,2,5,8],[3,4,7],[6]]=>9
[[1,3,4,8],[2,5,7],[6]]=>0
[[1,2,4,8],[3,5,7],[6]]=>9
[[1,2,3,8],[4,5,7],[6]]=>16
[[1,3,5,8],[2,4,6],[7]]=>0
[[1,2,5,8],[3,4,6],[7]]=>9
[[1,3,4,8],[2,5,6],[7]]=>0
[[1,2,4,8],[3,5,6],[7]]=>9
[[1,2,3,8],[4,5,6],[7]]=>16
[[1,4,6,7],[2,5,8],[3]]=>6
[[1,3,6,7],[2,5,8],[4]]=>0
[[1,2,6,7],[3,5,8],[4]]=>14
[[1,3,6,7],[2,4,8],[5]]=>0
[[1,2,6,7],[3,4,8],[5]]=>9
[[1,4,5,7],[2,6,8],[3]]=>6
[[1,3,5,7],[2,6,8],[4]]=>0
[[1,2,5,7],[3,6,8],[4]]=>16
[[1,3,4,7],[2,6,8],[5]]=>0
[[1,2,4,7],[3,6,8],[5]]=>11
[[1,2,3,7],[4,6,8],[5]]=>23
[[1,3,5,7],[2,4,8],[6]]=>0
[[1,2,5,7],[3,4,8],[6]]=>9
[[1,3,4,7],[2,5,8],[6]]=>0
[[1,2,4,7],[3,5,8],[6]]=>11
[[1,2,3,7],[4,5,8],[6]]=>19
[[1,4,5,6],[2,7,8],[3]]=>6
[[1,3,5,6],[2,7,8],[4]]=>0
[[1,2,5,6],[3,7,8],[4]]=>16
[[1,3,4,6],[2,7,8],[5]]=>0
[[1,2,4,6],[3,7,8],[5]]=>11
[[1,2,3,6],[4,7,8],[5]]=>23
[[1,3,4,5],[2,7,8],[6]]=>0
[[1,2,4,5],[3,7,8],[6]]=>11
[[1,2,3,5],[4,7,8],[6]]=>19
[[1,2,3,4],[5,7,8],[6]]=>28
[[1,3,5,6],[2,4,8],[7]]=>0
[[1,2,5,6],[3,4,8],[7]]=>9
[[1,3,4,6],[2,5,8],[7]]=>0
[[1,2,4,6],[3,5,8],[7]]=>11
[[1,2,3,6],[4,5,8],[7]]=>19
[[1,3,4,5],[2,6,8],[7]]=>0
[[1,2,4,5],[3,6,8],[7]]=>11
[[1,2,3,5],[4,6,8],[7]]=>19
[[1,2,3,4],[5,6,8],[7]]=>25
[[1,3,5,7],[2,4,6],[8]]=>0
[[1,2,5,7],[3,4,6],[8]]=>9
[[1,3,4,7],[2,5,6],[8]]=>0
[[1,2,4,7],[3,5,6],[8]]=>9
[[1,2,3,7],[4,5,6],[8]]=>16
[[1,3,5,6],[2,4,7],[8]]=>0
[[1,2,5,6],[3,4,7],[8]]=>9
[[1,3,4,6],[2,5,7],[8]]=>0
[[1,2,4,6],[3,5,7],[8]]=>11
[[1,2,3,6],[4,5,7],[8]]=>19
[[1,3,4,5],[2,6,7],[8]]=>0
[[1,2,4,5],[3,6,7],[8]]=>11
[[1,2,3,5],[4,6,7],[8]]=>19
[[1,2,3,4],[5,6,7],[8]]=>25
[[1,4,7,8],[2,5],[3,6]]=>7
[[1,3,7,8],[2,5],[4,6]]=>0
[[1,2,7,8],[3,5],[4,6]]=>12
[[1,3,7,8],[2,4],[5,6]]=>0
[[1,2,7,8],[3,4],[5,6]]=>7
[[1,4,6,8],[2,5],[3,7]]=>7
[[1,3,6,8],[2,5],[4,7]]=>0
[[1,2,6,8],[3,5],[4,7]]=>12
[[1,3,6,8],[2,4],[5,7]]=>0
[[1,2,6,8],[3,4],[5,7]]=>7
[[1,4,5,8],[2,6],[3,7]]=>7
[[1,3,5,8],[2,6],[4,7]]=>0
[[1,2,5,8],[3,6],[4,7]]=>17
[[1,3,4,8],[2,6],[5,7]]=>0
[[1,2,4,8],[3,6],[5,7]]=>11
[[1,2,3,8],[4,6],[5,7]]=>21
[[1,3,5,8],[2,4],[6,7]]=>0
[[1,2,5,8],[3,4],[6,7]]=>7
[[1,3,4,8],[2,5],[6,7]]=>0
[[1,2,4,8],[3,5],[6,7]]=>11
[[1,2,3,8],[4,5],[6,7]]=>17
[[1,4,6,7],[2,5],[3,8]]=>7
[[1,3,6,7],[2,5],[4,8]]=>0
[[1,2,6,7],[3,5],[4,8]]=>12
[[1,3,6,7],[2,4],[5,8]]=>0
[[1,2,6,7],[3,4],[5,8]]=>7
[[1,4,5,7],[2,6],[3,8]]=>7
[[1,3,5,7],[2,6],[4,8]]=>0
[[1,2,5,7],[3,6],[4,8]]=>17
[[1,3,4,7],[2,6],[5,8]]=>0
[[1,2,4,7],[3,6],[5,8]]=>11
[[1,2,3,7],[4,6],[5,8]]=>21
[[1,3,5,7],[2,4],[6,8]]=>0
[[1,2,5,7],[3,4],[6,8]]=>7
[[1,3,4,7],[2,5],[6,8]]=>0
[[1,2,4,7],[3,5],[6,8]]=>11
[[1,2,3,7],[4,5],[6,8]]=>17
[[1,4,5,6],[2,7],[3,8]]=>7
[[1,3,5,6],[2,7],[4,8]]=>0
[[1,2,5,6],[3,7],[4,8]]=>17
[[1,3,4,6],[2,7],[5,8]]=>0
[[1,2,4,6],[3,7],[5,8]]=>11
[[1,2,3,6],[4,7],[5,8]]=>25
[[1,3,4,5],[2,7],[6,8]]=>0
[[1,2,4,5],[3,7],[6,8]]=>11
[[1,2,3,5],[4,7],[6,8]]=>20
[[1,2,3,4],[5,7],[6,8]]=>28
[[1,3,5,6],[2,4],[7,8]]=>0
[[1,2,5,6],[3,4],[7,8]]=>7
[[1,3,4,6],[2,5],[7,8]]=>0
[[1,2,4,6],[3,5],[7,8]]=>11
[[1,2,3,6],[4,5],[7,8]]=>17
[[1,3,4,5],[2,6],[7,8]]=>0
[[1,2,4,5],[3,6],[7,8]]=>11
[[1,2,3,5],[4,6],[7,8]]=>20
[[1,2,3,4],[5,6],[7,8]]=>25
[[1,5,7,8],[2,6],[3],[4]]=>0
[[1,4,7,8],[2,6],[3],[5]]=>5
[[1,3,7,8],[2,6],[4],[5]]=>0
[[1,2,7,8],[3,6],[4],[5]]=>8
[[1,4,7,8],[2,5],[3],[6]]=>5
[[1,3,7,8],[2,5],[4],[6]]=>0
[[1,2,7,8],[3,5],[4],[6]]=>12
[[1,3,7,8],[2,4],[5],[6]]=>0
[[1,2,7,8],[3,4],[5],[6]]=>8
[[1,5,6,8],[2,7],[3],[4]]=>0
[[1,4,6,8],[2,7],[3],[5]]=>5
[[1,3,6,8],[2,7],[4],[5]]=>0
[[1,2,6,8],[3,7],[4],[5]]=>11
[[1,4,5,8],[2,7],[3],[6]]=>5
[[1,3,5,8],[2,7],[4],[6]]=>0
[[1,2,5,8],[3,7],[4],[6]]=>15
[[1,3,4,8],[2,7],[5],[6]]=>0
[[1,2,4,8],[3,7],[5],[6]]=>11
[[1,2,3,8],[4,7],[5],[6]]=>18
[[1,4,6,8],[2,5],[3],[7]]=>5
[[1,3,6,8],[2,5],[4],[7]]=>0
[[1,2,6,8],[3,5],[4],[7]]=>12
[[1,3,6,8],[2,4],[5],[7]]=>0
[[1,2,6,8],[3,4],[5],[7]]=>8
[[1,4,5,8],[2,6],[3],[7]]=>5
[[1,3,5,8],[2,6],[4],[7]]=>0
[[1,2,5,8],[3,6],[4],[7]]=>15
[[1,3,4,8],[2,6],[5],[7]]=>0
[[1,2,4,8],[3,6],[5],[7]]=>11
[[1,2,3,8],[4,6],[5],[7]]=>21
[[1,3,5,8],[2,4],[6],[7]]=>0
[[1,2,5,8],[3,4],[6],[7]]=>8
[[1,3,4,8],[2,5],[6],[7]]=>0
[[1,2,4,8],[3,5],[6],[7]]=>11
[[1,2,3,8],[4,5],[6],[7]]=>18
[[1,5,6,7],[2,8],[3],[4]]=>0
[[1,4,6,7],[2,8],[3],[5]]=>5
[[1,3,6,7],[2,8],[4],[5]]=>0
[[1,2,6,7],[3,8],[4],[5]]=>11
[[1,4,5,7],[2,8],[3],[6]]=>5
[[1,3,5,7],[2,8],[4],[6]]=>0
[[1,2,5,7],[3,8],[4],[6]]=>15
[[1,3,4,7],[2,8],[5],[6]]=>0
[[1,2,4,7],[3,8],[5],[6]]=>11
[[1,2,3,7],[4,8],[5],[6]]=>20
[[1,4,5,6],[2,8],[3],[7]]=>5
[[1,3,5,6],[2,8],[4],[7]]=>0
[[1,2,5,6],[3,8],[4],[7]]=>15
[[1,3,4,6],[2,8],[5],[7]]=>0
[[1,2,4,6],[3,8],[5],[7]]=>11
[[1,2,3,6],[4,8],[5],[7]]=>23
[[1,3,4,5],[2,8],[6],[7]]=>0
[[1,2,4,5],[3,8],[6],[7]]=>11
[[1,2,3,5],[4,8],[6],[7]]=>20
[[1,2,3,4],[5,8],[6],[7]]=>26
[[1,4,6,7],[2,5],[3],[8]]=>5
[[1,3,6,7],[2,5],[4],[8]]=>0
[[1,2,6,7],[3,5],[4],[8]]=>12
[[1,3,6,7],[2,4],[5],[8]]=>0
[[1,2,6,7],[3,4],[5],[8]]=>8
[[1,4,5,7],[2,6],[3],[8]]=>5
[[1,3,5,7],[2,6],[4],[8]]=>0
[[1,2,5,7],[3,6],[4],[8]]=>15
[[1,3,4,7],[2,6],[5],[8]]=>0
[[1,2,4,7],[3,6],[5],[8]]=>11
[[1,2,3,7],[4,6],[5],[8]]=>21
[[1,3,5,7],[2,4],[6],[8]]=>0
[[1,2,5,7],[3,4],[6],[8]]=>8
[[1,3,4,7],[2,5],[6],[8]]=>0
[[1,2,4,7],[3,5],[6],[8]]=>11
[[1,2,3,7],[4,5],[6],[8]]=>18
[[1,4,5,6],[2,7],[3],[8]]=>5
[[1,3,5,6],[2,7],[4],[8]]=>0
[[1,2,5,6],[3,7],[4],[8]]=>15
[[1,3,4,6],[2,7],[5],[8]]=>0
[[1,2,4,6],[3,7],[5],[8]]=>11
[[1,2,3,6],[4,7],[5],[8]]=>23
[[1,3,4,5],[2,7],[6],[8]]=>0
[[1,2,4,5],[3,7],[6],[8]]=>11
[[1,2,3,5],[4,7],[6],[8]]=>20
[[1,2,3,4],[5,7],[6],[8]]=>28
[[1,3,5,6],[2,4],[7],[8]]=>0
[[1,2,5,6],[3,4],[7],[8]]=>8
[[1,3,4,6],[2,5],[7],[8]]=>0
[[1,2,4,6],[3,5],[7],[8]]=>11
[[1,2,3,6],[4,5],[7],[8]]=>18
[[1,3,4,5],[2,6],[7],[8]]=>0
[[1,2,4,5],[3,6],[7],[8]]=>11
[[1,2,3,5],[4,6],[7],[8]]=>20
[[1,2,3,4],[5,6],[7],[8]]=>26
[[1,6,7,8],[2],[3],[4],[5]]=>4
[[1,5,7,8],[2],[3],[4],[6]]=>0
[[1,4,7,8],[2],[3],[5],[6]]=>4
[[1,3,7,8],[2],[4],[5],[6]]=>0
[[1,2,7,8],[3],[4],[5],[6]]=>14
[[1,5,6,8],[2],[3],[4],[7]]=>0
[[1,4,6,8],[2],[3],[5],[7]]=>4
[[1,3,6,8],[2],[4],[5],[7]]=>0
[[1,2,6,8],[3],[4],[5],[7]]=>11
[[1,4,5,8],[2],[3],[6],[7]]=>4
[[1,3,5,8],[2],[4],[6],[7]]=>0
[[1,2,5,8],[3],[4],[6],[7]]=>14
[[1,3,4,8],[2],[5],[6],[7]]=>0
[[1,2,4,8],[3],[5],[6],[7]]=>11
[[1,2,3,8],[4],[5],[6],[7]]=>22
[[1,5,6,7],[2],[3],[4],[8]]=>0
[[1,4,6,7],[2],[3],[5],[8]]=>4
[[1,3,6,7],[2],[4],[5],[8]]=>0
[[1,2,6,7],[3],[4],[5],[8]]=>11
[[1,4,5,7],[2],[3],[6],[8]]=>4
[[1,3,5,7],[2],[4],[6],[8]]=>0
[[1,2,5,7],[3],[4],[6],[8]]=>14
[[1,3,4,7],[2],[5],[6],[8]]=>0
[[1,2,4,7],[3],[5],[6],[8]]=>11
[[1,2,3,7],[4],[5],[6],[8]]=>20
[[1,4,5,6],[2],[3],[7],[8]]=>4
[[1,3,5,6],[2],[4],[7],[8]]=>0
[[1,2,5,6],[3],[4],[7],[8]]=>14
[[1,3,4,6],[2],[5],[7],[8]]=>0
[[1,2,4,6],[3],[5],[7],[8]]=>11
[[1,2,3,6],[4],[5],[7],[8]]=>22
[[1,3,4,5],[2],[6],[7],[8]]=>0
[[1,2,4,5],[3],[6],[7],[8]]=>11
[[1,2,3,5],[4],[6],[7],[8]]=>20
[[1,2,3,4],[5],[6],[7],[8]]=>28
[[1,4,7],[2,5,8],[3,6]]=>7
[[1,3,7],[2,5,8],[4,6]]=>0
[[1,2,7],[3,5,8],[4,6]]=>12
[[1,3,7],[2,4,8],[5,6]]=>0
[[1,2,7],[3,4,8],[5,6]]=>7
[[1,4,6],[2,5,8],[3,7]]=>7
[[1,3,6],[2,5,8],[4,7]]=>0
[[1,2,6],[3,5,8],[4,7]]=>12
[[1,3,6],[2,4,8],[5,7]]=>0
[[1,2,6],[3,4,8],[5,7]]=>7
[[1,4,5],[2,6,8],[3,7]]=>7
[[1,3,5],[2,6,8],[4,7]]=>0
[[1,2,5],[3,6,8],[4,7]]=>15
[[1,3,4],[2,6,8],[5,7]]=>0
[[1,2,4],[3,6,8],[5,7]]=>9
[[1,2,3],[4,6,8],[5,7]]=>19
[[1,3,5],[2,4,8],[6,7]]=>0
[[1,2,5],[3,4,8],[6,7]]=>7
[[1,3,4],[2,5,8],[6,7]]=>0
[[1,2,4],[3,5,8],[6,7]]=>9
[[1,2,3],[4,5,8],[6,7]]=>15
[[1,4,6],[2,5,7],[3,8]]=>7
[[1,3,6],[2,5,7],[4,8]]=>0
[[1,2,6],[3,5,7],[4,8]]=>15
[[1,3,6],[2,4,7],[5,8]]=>0
[[1,2,6],[3,4,7],[5,8]]=>9
[[1,4,5],[2,6,7],[3,8]]=>7
[[1,3,5],[2,6,7],[4,8]]=>0
[[1,2,5],[3,6,7],[4,8]]=>15
[[1,3,4],[2,6,7],[5,8]]=>0
[[1,2,4],[3,6,7],[5,8]]=>9
[[1,2,3],[4,6,7],[5,8]]=>19
[[1,3,5],[2,4,7],[6,8]]=>0
[[1,2,5],[3,4,7],[6,8]]=>9
[[1,3,4],[2,5,7],[6,8]]=>0
[[1,2,4],[3,5,7],[6,8]]=>9
[[1,2,3],[4,5,7],[6,8]]=>15
[[1,3,5],[2,4,6],[7,8]]=>0
[[1,2,5],[3,4,6],[7,8]]=>9
[[1,3,4],[2,5,6],[7,8]]=>0
[[1,2,4],[3,5,6],[7,8]]=>9
[[1,2,3],[4,5,6],[7,8]]=>15
[[1,5,7],[2,6,8],[3],[4]]=>0
[[1,4,7],[2,6,8],[3],[5]]=>5
[[1,3,7],[2,6,8],[4],[5]]=>0
[[1,2,7],[3,6,8],[4],[5]]=>9
[[1,4,7],[2,5,8],[3],[6]]=>5
[[1,3,7],[2,5,8],[4],[6]]=>0
[[1,2,7],[3,5,8],[4],[6]]=>13
[[1,3,7],[2,4,8],[5],[6]]=>0
[[1,2,7],[3,4,8],[5],[6]]=>9
[[1,5,6],[2,7,8],[3],[4]]=>0
[[1,4,6],[2,7,8],[3],[5]]=>5
[[1,3,6],[2,7,8],[4],[5]]=>0
[[1,2,6],[3,7,8],[4],[5]]=>9
[[1,4,5],[2,7,8],[3],[6]]=>5
[[1,3,5],[2,7,8],[4],[6]]=>0
[[1,2,5],[3,7,8],[4],[6]]=>13
[[1,3,4],[2,7,8],[5],[6]]=>0
[[1,2,4],[3,7,8],[5],[6]]=>9
[[1,2,3],[4,7,8],[5],[6]]=>16
[[1,4,6],[2,5,8],[3],[7]]=>5
[[1,3,6],[2,5,8],[4],[7]]=>0
[[1,2,6],[3,5,8],[4],[7]]=>13
[[1,3,6],[2,4,8],[5],[7]]=>0
[[1,2,6],[3,4,8],[5],[7]]=>9
[[1,4,5],[2,6,8],[3],[7]]=>5
[[1,3,5],[2,6,8],[4],[7]]=>0
[[1,2,5],[3,6,8],[4],[7]]=>13
[[1,3,4],[2,6,8],[5],[7]]=>0
[[1,2,4],[3,6,8],[5],[7]]=>9
[[1,2,3],[4,6,8],[5],[7]]=>19
[[1,3,5],[2,4,8],[6],[7]]=>0
[[1,2,5],[3,4,8],[6],[7]]=>9
[[1,3,4],[2,5,8],[6],[7]]=>0
[[1,2,4],[3,5,8],[6],[7]]=>9
[[1,2,3],[4,5,8],[6],[7]]=>16
[[1,4,6],[2,5,7],[3],[8]]=>5
[[1,3,6],[2,5,7],[4],[8]]=>0
[[1,2,6],[3,5,7],[4],[8]]=>13
[[1,3,6],[2,4,7],[5],[8]]=>0
[[1,2,6],[3,4,7],[5],[8]]=>9
[[1,4,5],[2,6,7],[3],[8]]=>5
[[1,3,5],[2,6,7],[4],[8]]=>0
[[1,2,5],[3,6,7],[4],[8]]=>13
[[1,3,4],[2,6,7],[5],[8]]=>0
[[1,2,4],[3,6,7],[5],[8]]=>9
[[1,2,3],[4,6,7],[5],[8]]=>19
[[1,3,5],[2,4,7],[6],[8]]=>0
[[1,2,5],[3,4,7],[6],[8]]=>9
[[1,3,4],[2,5,7],[6],[8]]=>0
[[1,2,4],[3,5,7],[6],[8]]=>9
[[1,2,3],[4,5,7],[6],[8]]=>16
[[1,3,5],[2,4,6],[7],[8]]=>0
[[1,2,5],[3,4,6],[7],[8]]=>9
[[1,3,4],[2,5,6],[7],[8]]=>0
[[1,2,4],[3,5,6],[7],[8]]=>9
[[1,2,3],[4,5,6],[7],[8]]=>16
[[1,5,8],[2,6],[3,7],[4]]=>0
[[1,4,8],[2,6],[3,7],[5]]=>5
[[1,3,8],[2,6],[4,7],[5]]=>0
[[1,2,8],[3,6],[4,7],[5]]=>7
[[1,4,8],[2,5],[3,7],[6]]=>5
[[1,3,8],[2,5],[4,7],[6]]=>0
[[1,2,8],[3,5],[4,7],[6]]=>11
[[1,3,8],[2,4],[5,7],[6]]=>0
[[1,2,8],[3,4],[5,7],[6]]=>7
[[1,4,8],[2,5],[3,6],[7]]=>7
[[1,3,8],[2,5],[4,6],[7]]=>0
[[1,2,8],[3,5],[4,6],[7]]=>11
[[1,3,8],[2,4],[5,6],[7]]=>0
[[1,2,8],[3,4],[5,6],[7]]=>7
[[1,5,7],[2,6],[3,8],[4]]=>0
[[1,4,7],[2,6],[3,8],[5]]=>5
[[1,3,7],[2,6],[4,8],[5]]=>0
[[1,2,7],[3,6],[4,8],[5]]=>7
[[1,4,7],[2,5],[3,8],[6]]=>5
[[1,3,7],[2,5],[4,8],[6]]=>0
[[1,2,7],[3,5],[4,8],[6]]=>11
[[1,3,7],[2,4],[5,8],[6]]=>0
[[1,2,7],[3,4],[5,8],[6]]=>7
[[1,5,6],[2,7],[3,8],[4]]=>0
[[1,4,6],[2,7],[3,8],[5]]=>5
[[1,3,6],[2,7],[4,8],[5]]=>0
[[1,2,6],[3,7],[4,8],[5]]=>10
[[1,4,5],[2,7],[3,8],[6]]=>5
[[1,3,5],[2,7],[4,8],[6]]=>0
[[1,2,5],[3,7],[4,8],[6]]=>14
[[1,3,4],[2,7],[5,8],[6]]=>0
[[1,2,4],[3,7],[5,8],[6]]=>10
[[1,2,3],[4,7],[5,8],[6]]=>16
[[1,4,6],[2,5],[3,8],[7]]=>5
[[1,3,6],[2,5],[4,8],[7]]=>0
[[1,2,6],[3,5],[4,8],[7]]=>11
[[1,3,6],[2,4],[5,8],[7]]=>0
[[1,2,6],[3,4],[5,8],[7]]=>7
[[1,4,5],[2,6],[3,8],[7]]=>5
[[1,3,5],[2,6],[4,8],[7]]=>0
[[1,2,5],[3,6],[4,8],[7]]=>14
[[1,3,4],[2,6],[5,8],[7]]=>0
[[1,2,4],[3,6],[5,8],[7]]=>10
[[1,2,3],[4,6],[5,8],[7]]=>19
[[1,3,5],[2,4],[6,8],[7]]=>0
[[1,2,5],[3,4],[6,8],[7]]=>7
[[1,3,4],[2,5],[6,8],[7]]=>0
[[1,2,4],[3,5],[6,8],[7]]=>10
[[1,2,3],[4,5],[6,8],[7]]=>16
[[1,4,7],[2,5],[3,6],[8]]=>7
[[1,3,7],[2,5],[4,6],[8]]=>0
[[1,2,7],[3,5],[4,6],[8]]=>11
[[1,3,7],[2,4],[5,6],[8]]=>0
[[1,2,7],[3,4],[5,6],[8]]=>7
[[1,4,6],[2,5],[3,7],[8]]=>7
[[1,3,6],[2,5],[4,7],[8]]=>0
[[1,2,6],[3,5],[4,7],[8]]=>11
[[1,3,6],[2,4],[5,7],[8]]=>0
[[1,2,6],[3,4],[5,7],[8]]=>7
[[1,4,5],[2,6],[3,7],[8]]=>7
[[1,3,5],[2,6],[4,7],[8]]=>0
[[1,2,5],[3,6],[4,7],[8]]=>16
[[1,3,4],[2,6],[5,7],[8]]=>0
[[1,2,4],[3,6],[5,7],[8]]=>10
[[1,2,3],[4,6],[5,7],[8]]=>19
[[1,3,5],[2,4],[6,7],[8]]=>0
[[1,2,5],[3,4],[6,7],[8]]=>7
[[1,3,4],[2,5],[6,7],[8]]=>0
[[1,2,4],[3,5],[6,7],[8]]=>10
[[1,2,3],[4,5],[6,7],[8]]=>16
[[1,6,8],[2,7],[3],[4],[5]]=>4
[[1,5,8],[2,7],[3],[4],[6]]=>0
[[1,4,8],[2,7],[3],[5],[6]]=>4
[[1,3,8],[2,7],[4],[5],[6]]=>0
[[1,2,8],[3,7],[4],[5],[6]]=>11
[[1,5,8],[2,6],[3],[4],[7]]=>0
[[1,4,8],[2,6],[3],[5],[7]]=>4
[[1,3,8],[2,6],[4],[5],[7]]=>0
[[1,2,8],[3,6],[4],[5],[7]]=>8
[[1,4,8],[2,5],[3],[6],[7]]=>4
[[1,3,8],[2,5],[4],[6],[7]]=>0
[[1,2,8],[3,5],[4],[6],[7]]=>11
[[1,3,8],[2,4],[5],[6],[7]]=>0
[[1,2,8],[3,4],[5],[6],[7]]=>8
[[1,6,7],[2,8],[3],[4],[5]]=>4
[[1,5,7],[2,8],[3],[4],[6]]=>0
[[1,4,7],[2,8],[3],[5],[6]]=>4
[[1,3,7],[2,8],[4],[5],[6]]=>0
[[1,2,7],[3,8],[4],[5],[6]]=>13
[[1,5,6],[2,8],[3],[4],[7]]=>0
[[1,4,6],[2,8],[3],[5],[7]]=>4
[[1,3,6],[2,8],[4],[5],[7]]=>0
[[1,2,6],[3,8],[4],[5],[7]]=>10
[[1,4,5],[2,8],[3],[6],[7]]=>4
[[1,3,5],[2,8],[4],[6],[7]]=>0
[[1,2,5],[3,8],[4],[6],[7]]=>13
[[1,3,4],[2,8],[5],[6],[7]]=>0
[[1,2,4],[3,8],[5],[6],[7]]=>10
[[1,2,3],[4,8],[5],[6],[7]]=>19
[[1,5,7],[2,6],[3],[4],[8]]=>0
[[1,4,7],[2,6],[3],[5],[8]]=>4
[[1,3,7],[2,6],[4],[5],[8]]=>0
[[1,2,7],[3,6],[4],[5],[8]]=>8
[[1,4,7],[2,5],[3],[6],[8]]=>4
[[1,3,7],[2,5],[4],[6],[8]]=>0
[[1,2,7],[3,5],[4],[6],[8]]=>11
[[1,3,7],[2,4],[5],[6],[8]]=>0
[[1,2,7],[3,4],[5],[6],[8]]=>8
[[1,5,6],[2,7],[3],[4],[8]]=>0
[[1,4,6],[2,7],[3],[5],[8]]=>4
[[1,3,6],[2,7],[4],[5],[8]]=>0
[[1,2,6],[3,7],[4],[5],[8]]=>10
[[1,4,5],[2,7],[3],[6],[8]]=>4
[[1,3,5],[2,7],[4],[6],[8]]=>0
[[1,2,5],[3,7],[4],[6],[8]]=>13
[[1,3,4],[2,7],[5],[6],[8]]=>0
[[1,2,4],[3,7],[5],[6],[8]]=>10
[[1,2,3],[4,7],[5],[6],[8]]=>17
[[1,4,6],[2,5],[3],[7],[8]]=>4
[[1,3,6],[2,5],[4],[7],[8]]=>0
[[1,2,6],[3,5],[4],[7],[8]]=>11
[[1,3,6],[2,4],[5],[7],[8]]=>0
[[1,2,6],[3,4],[5],[7],[8]]=>8
[[1,4,5],[2,6],[3],[7],[8]]=>4
[[1,3,5],[2,6],[4],[7],[8]]=>0
[[1,2,5],[3,6],[4],[7],[8]]=>13
[[1,3,4],[2,6],[5],[7],[8]]=>0
[[1,2,4],[3,6],[5],[7],[8]]=>10
[[1,2,3],[4,6],[5],[7],[8]]=>19
[[1,3,5],[2,4],[6],[7],[8]]=>0
[[1,2,5],[3,4],[6],[7],[8]]=>8
[[1,3,4],[2,5],[6],[7],[8]]=>0
[[1,2,4],[3,5],[6],[7],[8]]=>10
[[1,2,3],[4,5],[6],[7],[8]]=>17
[[1,7,8],[2],[3],[4],[5],[6]]=>0
[[1,6,8],[2],[3],[4],[5],[7]]=>3
[[1,5,8],[2],[3],[4],[6],[7]]=>0
[[1,4,8],[2],[3],[5],[6],[7]]=>3
[[1,3,8],[2],[4],[5],[6],[7]]=>0
[[1,2,8],[3],[4],[5],[6],[7]]=>10
[[1,6,7],[2],[3],[4],[5],[8]]=>3
[[1,5,7],[2],[3],[4],[6],[8]]=>0
[[1,4,7],[2],[3],[5],[6],[8]]=>3
[[1,3,7],[2],[4],[5],[6],[8]]=>0
[[1,2,7],[3],[4],[5],[6],[8]]=>12
[[1,5,6],[2],[3],[4],[7],[8]]=>0
[[1,4,6],[2],[3],[5],[7],[8]]=>3
[[1,3,6],[2],[4],[5],[7],[8]]=>0
[[1,2,6],[3],[4],[5],[7],[8]]=>10
[[1,4,5],[2],[3],[6],[7],[8]]=>3
[[1,3,5],[2],[4],[6],[7],[8]]=>0
[[1,2,5],[3],[4],[6],[7],[8]]=>12
[[1,3,4],[2],[5],[6],[7],[8]]=>0
[[1,2,4],[3],[5],[6],[7],[8]]=>10
[[1,2,3],[4],[5],[6],[7],[8]]=>18
[[1,5],[2,6],[3,7],[4,8]]=>0
[[1,4],[2,6],[3,7],[5,8]]=>6
[[1,3],[2,6],[4,7],[5,8]]=>0
[[1,2],[3,6],[4,7],[5,8]]=>6
[[1,4],[2,5],[3,7],[6,8]]=>6
[[1,3],[2,5],[4,7],[6,8]]=>0
[[1,2],[3,5],[4,7],[6,8]]=>10
[[1,3],[2,4],[5,7],[6,8]]=>0
[[1,2],[3,4],[5,7],[6,8]]=>6
[[1,4],[2,5],[3,6],[7,8]]=>6
[[1,3],[2,5],[4,6],[7,8]]=>0
[[1,2],[3,5],[4,6],[7,8]]=>10
[[1,3],[2,4],[5,6],[7,8]]=>0
[[1,2],[3,4],[5,6],[7,8]]=>6
[[1,6],[2,7],[3,8],[4],[5]]=>4
[[1,5],[2,7],[3,8],[4],[6]]=>0
[[1,4],[2,7],[3,8],[5],[6]]=>4
[[1,3],[2,7],[4,8],[5],[6]]=>0
[[1,2],[3,7],[4,8],[5],[6]]=>10
[[1,5],[2,6],[3,8],[4],[7]]=>0
[[1,4],[2,6],[3,8],[5],[7]]=>4
[[1,3],[2,6],[4,8],[5],[7]]=>0
[[1,2],[3,6],[4,8],[5],[7]]=>7
[[1,4],[2,5],[3,8],[6],[7]]=>4
[[1,3],[2,5],[4,8],[6],[7]]=>0
[[1,2],[3,5],[4,8],[6],[7]]=>10
[[1,3],[2,4],[5,8],[6],[7]]=>0
[[1,2],[3,4],[5,8],[6],[7]]=>7
[[1,5],[2,6],[3,7],[4],[8]]=>0
[[1,4],[2,6],[3,7],[5],[8]]=>4
[[1,3],[2,6],[4,7],[5],[8]]=>0
[[1,2],[3,6],[4,7],[5],[8]]=>7
[[1,4],[2,5],[3,7],[6],[8]]=>4
[[1,3],[2,5],[4,7],[6],[8]]=>0
[[1,2],[3,5],[4,7],[6],[8]]=>10
[[1,3],[2,4],[5,7],[6],[8]]=>0
[[1,2],[3,4],[5,7],[6],[8]]=>7
[[1,4],[2,5],[3,6],[7],[8]]=>7
[[1,3],[2,5],[4,6],[7],[8]]=>0
[[1,2],[3,5],[4,6],[7],[8]]=>10
[[1,3],[2,4],[5,6],[7],[8]]=>0
[[1,2],[3,4],[5,6],[7],[8]]=>7
[[1,7],[2,8],[3],[4],[5],[6]]=>0
[[1,6],[2,8],[3],[4],[5],[7]]=>3
[[1,5],[2,8],[3],[4],[6],[7]]=>0
[[1,4],[2,8],[3],[5],[6],[7]]=>3
[[1,3],[2,8],[4],[5],[6],[7]]=>0
[[1,2],[3,8],[4],[5],[6],[7]]=>8
[[1,6],[2,7],[3],[4],[5],[8]]=>3
[[1,5],[2,7],[3],[4],[6],[8]]=>0
[[1,4],[2,7],[3],[5],[6],[8]]=>3
[[1,3],[2,7],[4],[5],[6],[8]]=>0
[[1,2],[3,7],[4],[5],[6],[8]]=>10
[[1,5],[2,6],[3],[4],[7],[8]]=>0
[[1,4],[2,6],[3],[5],[7],[8]]=>3
[[1,3],[2,6],[4],[5],[7],[8]]=>0
[[1,2],[3,6],[4],[5],[7],[8]]=>8
[[1,4],[2,5],[3],[6],[7],[8]]=>3
[[1,3],[2,5],[4],[6],[7],[8]]=>0
[[1,2],[3,5],[4],[6],[7],[8]]=>10
[[1,3],[2,4],[5],[6],[7],[8]]=>0
[[1,2],[3,4],[5],[6],[7],[8]]=>8
[[1,8],[2],[3],[4],[5],[6],[7]]=>2
[[1,7],[2],[3],[4],[5],[6],[8]]=>0
[[1,6],[2],[3],[4],[5],[7],[8]]=>2
[[1,5],[2],[3],[4],[6],[7],[8]]=>0
[[1,4],[2],[3],[5],[6],[7],[8]]=>2
[[1,3],[2],[4],[5],[6],[7],[8]]=>0
[[1,2],[3],[4],[5],[6],[7],[8]]=>10
[[1],[2],[3],[4],[5],[6],[7],[8]]=>0
[[1,2,3,4,5,6,7,8,9]]=>81
[[1,2,3,4,5,6,7,8],[9]]=>70
[[1,2,3,4,5,6,7],[8,9]]=>59
[[1,2,3,4,5,6,7],[8],[9]]=>61
[[1,3,4,5,6,7,8,9],[2]]=>0
[[1,2,5,6,7,8,9],[3,4]]=>9
[[1,4,5,6,7,8,9],[2],[3]]=>7
[[1,2,3,7,8,9],[4,5,6]]=>18
[[1,3,5,7,8,9],[2,4,6]]=>0
[[1,3,5,6,7,8,9],[2,4]]=>0
[[1,2,3,4,5,6,8],[7,9]]=>55
[[1,2,3,4,5,6,7,9],[8]]=>66
[[1,2,3,4,5,6,9],[7,8]]=>53
[[1,2,3,4,5,6,9],[7],[8]]=>57
[[1,2,4,5,6,7,8,9],[3]]=>16
[[1,3,4,6,7,8,9],[2,5]]=>0
[[1,3,5,6,7,8,9],[2],[4]]=>0
[[1,3,5,6,8,9],[2,4,7]]=>0
[[1,3,4,5,6,7,8],[2,9]]=>0
[[1,3,4,5,6,7,8],[2],[9]]=>0
[[1,2,3,6,7,8,9],[4,5]]=>23
[[1,2,5,6,7,8,9],[3],[4]]=>21
[[1,2,3,4,8,9],[5,6,7]]=>30
[[1,2,3,4,7,8,9],[5,6]]=>35
[[1,2,3,4,5,6,8],[7],[9]]=>55
[[1,2,3,5,7,9],[4,6,8]]=>26
[[1,2,3,4,5,7,9],[6,8]]=>48
[[1,2,4,6,8,9],[3,5,7]]=>14
[[1,2,4,6,7,8,9],[3,5]]=>15
[[1,2,4,5,6,7,8],[3,9]]=>15
[[1,3,4,5,7,9],[2,6,8]]=>0
[[1,3,4,5,6,7,9],[2,8]]=>0
[[1,2,3,5,6,7,8,9],[4]]=>30
[[1,2,4,5,7,8,9],[3,6]]=>15
[[1,2,4,6,7,8,9],[3],[5]]=>15
[[1,2,4,6,7,9],[3,5,8]]=>14
[[1,2,3,5,6,7,8],[4,9]]=>28
[[1,2,4,5,6,7,8],[3],[9]]=>15
[[1,2,3,4,5,6,8,9],[7]]=>60
[[1,2,3,4,5,7,8,9],[6]]=>52
[[1,2,3,4,6,7,8,9],[5]]=>42
[[1,2,3,4,5,8,9],[6,7]]=>45
[[1,2,3,4,5,8,9],[6],[7]]=>51
[[1,2,3,4,7,8,9],[5],[6]]=>43
[[1,2,3,6,7,8,9],[4],[5]]=>33
[[1,3,4,7,8,9],[2,5,6]]=>0
[[1,3,4,5,7,8,9],[2,6]]=>0
[[1,3,4,6,7,8,9],[2],[5]]=>0
[[1,3,5,6,7,9],[2,4,8]]=>0
[[1,2,3,4,5,7,8],[6],[9]]=>48
[[1,2,3,4,6,7,8],[5],[9]]=>39
[[1,2,3,5,6,7,8],[4],[9]]=>28
[[1,2,3,4,5,7,8],[6,9]]=>48
[[1,3,4,5,6,8,9],[2,7]]=>0
[[1,2,3,4,6,7,8],[5,9]]=>39
[[1,2,5,7,8,9],[3,4,6]]=>10
[[1,3,4,5,6,7,9],[2],[8]]=>0
[[1,3,4,5,6,8,9],[2],[7]]=>0
[[1,3,4,5,8,9],[2,6,7]]=>0
[[1,2,3,5,7,8,9],[4,6]]=>28
[[1,3,4,5,7,8,9],[2],[6]]=>0
[[1,2,3,6,8,9],[4,5,7]]=>23
[[1,2,3,4,6,8,9],[5,7]]=>39
[[1,2,4,7,8,9],[3,5,6]]=>10
[[1,2,3,4,5,7,9],[6],[8]]=>48
[[1,2,3,5,8,9],[4,6,7]]=>23
[[1,2,4,5,6,7,9],[3],[8]]=>15
[[1,2,3,4,6,8,9],[5],[7]]=>39
[[1,2,5,6,8,9],[3,4,7]]=>10
[[1,2,5,6,7,9],[3,4,8]]=>10
[[1,2,3,4,6,7,9],[5],[8]]=>39
[[1,2,3,5,6,7,9],[4,8]]=>28
[[1,2,3,5,6,8,9],[4,7]]=>28
[[1,2,3,4,6,7,9],[5,8]]=>39
[[1,2,4,5,8,9],[3,6,7]]=>14
[[1,2,4,5,6,7,9],[3,8]]=>15
[[1,2,4,5,7,9],[3,6,8]]=>14
[[1,2,3,5,6,8,9],[4],[7]]=>28
[[1,2,4,5,7,8,9],[3],[6]]=>15
[[1,2,3,5,7,8,9],[4],[6]]=>28
[[1,2,4,5,6,8,9],[3],[7]]=>15
[[1,3,4,6,7,9],[2,5,8]]=>0
[[1,3,4,6,8,9],[2,5,7]]=>0
[[1,2,4,5,6,8,9],[3,7]]=>15
[[1,2,3,6,7,9],[4,5,8]]=>23
[[1,2,3,5,6,7,9],[4],[8]]=>28
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
Eigenvalues of the random-to-random operator acting on a simple module.
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module [1].
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module [1].
References
[1] Dieker, A. B., Saliola, F. Spectral analysis of random-to-random Markov chains arXiv:1509.08580
[2] Eigenvalues of the random-to-random operator acting on the regular representation Eigenvalues of the random-to-random operator acting on the regular representation. St000500
[3] The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000046
[2] Eigenvalues of the random-to-random operator acting on the regular representation Eigenvalues of the random-to-random operator acting on the regular representation. St000500
[3] The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000046
Code
def diagonal_index_of_partition(la):
return sum((j - i) for (i, j) in la.cells())
def binomial_shifted_diagonal_index_of_partition(partition):
return binomial(partition.size() + 1, 2) + diagonal_index_of_partition(partition)
def is_desarrangement_tableau(t):
if t.size() == 0:
return True
descents = t.standard_descents()
ascents = [i for i in t.entries() if i not in descents]
return min(ascents) % 2 == 0
def r2r_statistic_on_standard_tableaux(t):
# remove 1 and rectify until we get a desarrangement tableau
s = copy(t)
while not is_desarrangement_tableau(s):
s = SkewTableau([[(i-1 if i > 1 else None) for i in row] for row in s])
s = StandardTableau(s.rectify())
b_t = binomial_shifted_diagonal_index_of_partition(t.shape())
b_s = binomial_shifted_diagonal_index_of_partition(s.shape())
return b_t - b_s
def statistic(t):
return r2r_statistic_on_standard_tableaux(t)
Created
May 25, 2016 at 18:06 by Franco Saliola
Updated
Mar 15, 2021 at 11:33 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!