- FindStat

edit this statistic or download as text // json

Identifier

St000693: Standard tableaux ⟶ ℤ

Values

=>
                            Cc0007;cc-rep
                            
                            
                            

                        [[1,2]]=>0
[[1],[2]]=>1
[[1,2,3]]=>0
[[1,3],[2]]=>1
[[1,2],[3]]=>2
[[1],[2],[3]]=>0
[[1,2,3,4]]=>0
[[1,3,4],[2]]=>1
[[1,2,4],[3]]=>2
[[1,2,3],[4]]=>3
[[1,3],[2,4]]=>0
[[1,2],[3,4]]=>2
[[1,4],[2],[3]]=>3
[[1,3],[2],[4]]=>0
[[1,2],[3],[4]]=>1
[[1],[2],[3],[4]]=>2
[[1,2,3,4,5]]=>0
[[1,3,4,5],[2]]=>1
[[1,2,4,5],[3]]=>2
[[1,2,3,5],[4]]=>3
[[1,2,3,4],[5]]=>4
[[1,3,5],[2,4]]=>4
[[1,2,5],[3,4]]=>2
[[1,3,4],[2,5]]=>0
[[1,2,4],[3,5]]=>1
[[1,2,3],[4,5]]=>3
[[1,4,5],[2],[3]]=>3
[[1,3,5],[2],[4]]=>4
[[1,2,5],[3],[4]]=>0
[[1,3,4],[2],[5]]=>0
[[1,2,4],[3],[5]]=>1
[[1,2,3],[4],[5]]=>2
[[1,4],[2,5],[3]]=>2
[[1,3],[2,5],[4]]=>4
[[1,2],[3,5],[4]]=>0
[[1,3],[2,4],[5]]=>3
[[1,2],[3,4],[5]]=>1
[[1,5],[2],[3],[4]]=>1
[[1,4],[2],[3],[5]]=>2
[[1,3],[2],[4],[5]]=>3
[[1,2],[3],[4],[5]]=>4
[[1],[2],[3],[4],[5]]=>0
[[1,2,3,4,5,6]]=>0
[[1,3,4,5,6],[2]]=>1
[[1,2,4,5,6],[3]]=>2
[[1,2,3,5,6],[4]]=>3
[[1,2,3,4,6],[5]]=>4
[[1,2,3,4,5],[6]]=>5
[[1,3,5,6],[2,4]]=>4
[[1,2,5,6],[3,4]]=>2
[[1,3,4,6],[2,5]]=>5
[[1,2,4,6],[3,5]]=>0
[[1,2,3,6],[4,5]]=>3
[[1,3,4,5],[2,6]]=>0
[[1,2,4,5],[3,6]]=>1
[[1,2,3,5],[4,6]]=>2
[[1,2,3,4],[5,6]]=>4
[[1,4,5,6],[2],[3]]=>3
[[1,3,5,6],[2],[4]]=>4
[[1,2,5,6],[3],[4]]=>5
[[1,3,4,6],[2],[5]]=>5
[[1,2,4,6],[3],[5]]=>0
[[1,2,3,6],[4],[5]]=>1
[[1,3,4,5],[2],[6]]=>0
[[1,2,4,5],[3],[6]]=>1
[[1,2,3,5],[4],[6]]=>2
[[1,2,3,4],[5],[6]]=>3
[[1,3,5],[2,4,6]]=>3
[[1,2,5],[3,4,6]]=>1
[[1,3,4],[2,5,6]]=>5
[[1,2,4],[3,5,6]]=>0
[[1,2,3],[4,5,6]]=>3
[[1,4,6],[2,5],[3]]=>1
[[1,3,6],[2,5],[4]]=>4
[[1,2,6],[3,5],[4]]=>5
[[1,3,6],[2,4],[5]]=>2
[[1,2,6],[3,4],[5]]=>0
[[1,4,5],[2,6],[3]]=>2
[[1,3,5],[2,6],[4]]=>3
[[1,2,5],[3,6],[4]]=>4
[[1,3,4],[2,6],[5]]=>5
[[1,2,4],[3,6],[5]]=>0
[[1,2,3],[4,6],[5]]=>1
[[1,3,5],[2,4],[6]]=>3
[[1,2,5],[3,4],[6]]=>1
[[1,3,4],[2,5],[6]]=>4
[[1,2,4],[3,5],[6]]=>5
[[1,2,3],[4,5],[6]]=>2
[[1,5,6],[2],[3],[4]]=>0
[[1,4,6],[2],[3],[5]]=>1
[[1,3,6],[2],[4],[5]]=>2
[[1,2,6],[3],[4],[5]]=>3
[[1,4,5],[2],[3],[6]]=>2
[[1,3,5],[2],[4],[6]]=>3
[[1,2,5],[3],[4],[6]]=>4
[[1,3,4],[2],[5],[6]]=>4
[[1,2,4],[3],[5],[6]]=>5
[[1,2,3],[4],[5],[6]]=>0
[[1,4],[2,5],[3,6]]=>0
[[1,3],[2,5],[4,6]]=>3
[[1,2],[3,5],[4,6]]=>4
[[1,3],[2,4],[5,6]]=>2
[[1,2],[3,4],[5,6]]=>0
[[1,5],[2,6],[3],[4]]=>5
[[1,4],[2,6],[3],[5]]=>1
[[1,3],[2,6],[4],[5]]=>2
[[1,2],[3,6],[4],[5]]=>3
[[1,4],[2,5],[3],[6]]=>0
[[1,3],[2,5],[4],[6]]=>3
[[1,2],[3,5],[4],[6]]=>4
[[1,3],[2,4],[5],[6]]=>1
[[1,2],[3,4],[5],[6]]=>5
[[1,6],[2],[3],[4],[5]]=>4
[[1,5],[2],[3],[4],[6]]=>5
[[1,4],[2],[3],[5],[6]]=>0
[[1,3],[2],[4],[5],[6]]=>1
[[1,2],[3],[4],[5],[6]]=>2
[[1],[2],[3],[4],[5],[6]]=>3
[[1,2,3,4,5,6,7]]=>0
[[1,3,4,5,6,7],[2]]=>1
[[1,2,4,5,6,7],[3]]=>2
[[1,2,3,5,6,7],[4]]=>3
[[1,2,3,4,6,7],[5]]=>4
[[1,2,3,4,5,7],[6]]=>5
[[1,2,3,4,5,6],[7]]=>6
[[1,3,5,6,7],[2,4]]=>4
[[1,2,5,6,7],[3,4]]=>2
[[1,3,4,6,7],[2,5]]=>5
[[1,2,4,6,7],[3,5]]=>6
[[1,2,3,6,7],[4,5]]=>3
[[1,3,4,5,7],[2,6]]=>6
[[1,2,4,5,7],[3,6]]=>0
[[1,2,3,5,7],[4,6]]=>1
[[1,2,3,4,7],[5,6]]=>4
[[1,3,4,5,6],[2,7]]=>0
[[1,2,4,5,6],[3,7]]=>1
[[1,2,3,5,6],[4,7]]=>2
[[1,2,3,4,6],[5,7]]=>3
[[1,2,3,4,5],[6,7]]=>5
[[1,4,5,6,7],[2],[3]]=>3
[[1,3,5,6,7],[2],[4]]=>4
[[1,2,5,6,7],[3],[4]]=>5
[[1,3,4,6,7],[2],[5]]=>5
[[1,2,4,6,7],[3],[5]]=>6
[[1,2,3,6,7],[4],[5]]=>0
[[1,3,4,5,7],[2],[6]]=>6
[[1,2,4,5,7],[3],[6]]=>0
[[1,2,3,5,7],[4],[6]]=>1
[[1,2,3,4,7],[5],[6]]=>2
[[1,3,4,5,6],[2],[7]]=>0
[[1,2,4,5,6],[3],[7]]=>1
[[1,2,3,5,6],[4],[7]]=>2
[[1,2,3,4,6],[5],[7]]=>3
[[1,2,3,4,5],[6],[7]]=>4
[[1,3,5,7],[2,4,6]]=>2
[[1,2,5,7],[3,4,6]]=>0
[[1,3,4,7],[2,5,6]]=>5
[[1,2,4,7],[3,5,6]]=>6
[[1,2,3,7],[4,5,6]]=>3
[[1,3,5,6],[2,4,7]]=>3
[[1,2,5,6],[3,4,7]]=>1
[[1,3,4,6],[2,5,7]]=>4
[[1,2,4,6],[3,5,7]]=>5
[[1,2,3,6],[4,5,7]]=>2
[[1,3,4,5],[2,6,7]]=>6
[[1,2,4,5],[3,6,7]]=>0
[[1,2,3,5],[4,6,7]]=>1
[[1,2,3,4],[5,6,7]]=>4
[[1,4,6,7],[2,5],[3]]=>0
[[1,3,6,7],[2,5],[4]]=>4
[[1,2,6,7],[3,5],[4]]=>5
[[1,3,6,7],[2,4],[5]]=>1
[[1,2,6,7],[3,4],[5]]=>6
[[1,4,5,7],[2,6],[3]]=>1
[[1,3,5,7],[2,6],[4]]=>2
[[1,2,5,7],[3,6],[4]]=>3
[[1,3,4,7],[2,6],[5]]=>5
[[1,2,4,7],[3,6],[5]]=>6
[[1,2,3,7],[4,6],[5]]=>0
[[1,3,5,7],[2,4],[6]]=>2
[[1,2,5,7],[3,4],[6]]=>0
[[1,3,4,7],[2,5],[6]]=>3
[[1,2,4,7],[3,5],[6]]=>4
[[1,2,3,7],[4,5],[6]]=>1
[[1,4,5,6],[2,7],[3]]=>2
[[1,3,5,6],[2,7],[4]]=>3
[[1,2,5,6],[3,7],[4]]=>4
[[1,3,4,6],[2,7],[5]]=>4
[[1,2,4,6],[3,7],[5]]=>5
[[1,2,3,6],[4,7],[5]]=>6
[[1,3,4,5],[2,7],[6]]=>6
[[1,2,4,5],[3,7],[6]]=>0
[[1,2,3,5],[4,7],[6]]=>1
[[1,2,3,4],[5,7],[6]]=>2
[[1,3,5,6],[2,4],[7]]=>3
[[1,2,5,6],[3,4],[7]]=>1
[[1,3,4,6],[2,5],[7]]=>4
[[1,2,4,6],[3,5],[7]]=>5
[[1,2,3,6],[4,5],[7]]=>2
[[1,3,4,5],[2,6],[7]]=>5
[[1,2,4,5],[3,6],[7]]=>6
[[1,2,3,5],[4,6],[7]]=>0
[[1,2,3,4],[5,6],[7]]=>3
[[1,5,6,7],[2],[3],[4]]=>6
[[1,4,6,7],[2],[3],[5]]=>0
[[1,3,6,7],[2],[4],[5]]=>1
[[1,2,6,7],[3],[4],[5]]=>2
[[1,4,5,7],[2],[3],[6]]=>1
[[1,3,5,7],[2],[4],[6]]=>2
[[1,2,5,7],[3],[4],[6]]=>3
[[1,3,4,7],[2],[5],[6]]=>3
[[1,2,4,7],[3],[5],[6]]=>4
[[1,2,3,7],[4],[5],[6]]=>5
[[1,4,5,6],[2],[3],[7]]=>2
[[1,3,5,6],[2],[4],[7]]=>3
[[1,2,5,6],[3],[4],[7]]=>4
[[1,3,4,6],[2],[5],[7]]=>4
[[1,2,4,6],[3],[5],[7]]=>5
[[1,2,3,6],[4],[5],[7]]=>6
[[1,3,4,5],[2],[6],[7]]=>5
[[1,2,4,5],[3],[6],[7]]=>6
[[1,2,3,5],[4],[6],[7]]=>0
[[1,2,3,4],[5],[6],[7]]=>1
[[1,4,6],[2,5,7],[3]]=>6
[[1,3,6],[2,5,7],[4]]=>3
[[1,2,6],[3,5,7],[4]]=>4
[[1,3,6],[2,4,7],[5]]=>0
[[1,2,6],[3,4,7],[5]]=>5
[[1,4,5],[2,6,7],[3]]=>1
[[1,3,5],[2,6,7],[4]]=>2
[[1,2,5],[3,6,7],[4]]=>3
[[1,3,4],[2,6,7],[5]]=>5
[[1,2,4],[3,6,7],[5]]=>6
[[1,2,3],[4,6,7],[5]]=>0
[[1,3,5],[2,4,7],[6]]=>2
[[1,2,5],[3,4,7],[6]]=>0
[[1,3,4],[2,5,7],[6]]=>3
[[1,2,4],[3,5,7],[6]]=>4
[[1,2,3],[4,5,7],[6]]=>1
[[1,3,5],[2,4,6],[7]]=>1
[[1,2,5],[3,4,6],[7]]=>6
[[1,3,4],[2,5,6],[7]]=>4
[[1,2,4],[3,5,6],[7]]=>5
[[1,2,3],[4,5,6],[7]]=>2
[[1,4,7],[2,5],[3,6]]=>5
[[1,3,7],[2,5],[4,6]]=>2
[[1,2,7],[3,5],[4,6]]=>3
[[1,3,7],[2,4],[5,6]]=>1
[[1,2,7],[3,4],[5,6]]=>6
[[1,4,6],[2,5],[3,7]]=>6
[[1,3,6],[2,5],[4,7]]=>3
[[1,2,6],[3,5],[4,7]]=>4
[[1,3,6],[2,4],[5,7]]=>0
[[1,2,6],[3,4],[5,7]]=>5
[[1,4,5],[2,6],[3,7]]=>0
[[1,3,5],[2,6],[4,7]]=>1
[[1,2,5],[3,6],[4,7]]=>2
[[1,3,4],[2,6],[5,7]]=>4
[[1,2,4],[3,6],[5,7]]=>5
[[1,2,3],[4,6],[5,7]]=>6
[[1,3,5],[2,4],[6,7]]=>2
[[1,2,5],[3,4],[6,7]]=>0
[[1,3,4],[2,5],[6,7]]=>3
[[1,2,4],[3,5],[6,7]]=>4
[[1,2,3],[4,5],[6,7]]=>1
[[1,5,7],[2,6],[3],[4]]=>4
[[1,4,7],[2,6],[3],[5]]=>0
[[1,3,7],[2,6],[4],[5]]=>1
[[1,2,7],[3,6],[4],[5]]=>2
[[1,4,7],[2,5],[3],[6]]=>5
[[1,3,7],[2,5],[4],[6]]=>2
[[1,2,7],[3,5],[4],[6]]=>3
[[1,3,7],[2,4],[5],[6]]=>6
[[1,2,7],[3,4],[5],[6]]=>4
[[1,5,6],[2,7],[3],[4]]=>5
[[1,4,6],[2,7],[3],[5]]=>6
[[1,3,6],[2,7],[4],[5]]=>0
[[1,2,6],[3,7],[4],[5]]=>1
[[1,4,5],[2,7],[3],[6]]=>1
[[1,3,5],[2,7],[4],[6]]=>2
[[1,2,5],[3,7],[4],[6]]=>3
[[1,3,4],[2,7],[5],[6]]=>3
[[1,2,4],[3,7],[5],[6]]=>4
[[1,2,3],[4,7],[5],[6]]=>5
[[1,4,6],[2,5],[3],[7]]=>6
[[1,3,6],[2,5],[4],[7]]=>3
[[1,2,6],[3,5],[4],[7]]=>4
[[1,3,6],[2,4],[5],[7]]=>0
[[1,2,6],[3,4],[5],[7]]=>5
[[1,4,5],[2,6],[3],[7]]=>0
[[1,3,5],[2,6],[4],[7]]=>1
[[1,2,5],[3,6],[4],[7]]=>2
[[1,3,4],[2,6],[5],[7]]=>4
[[1,2,4],[3,6],[5],[7]]=>5
[[1,2,3],[4,6],[5],[7]]=>6
[[1,3,5],[2,4],[6],[7]]=>1
[[1,2,5],[3,4],[6],[7]]=>6
[[1,3,4],[2,5],[6],[7]]=>2
[[1,2,4],[3,5],[6],[7]]=>3
[[1,2,3],[4,5],[6],[7]]=>0
[[1,6,7],[2],[3],[4],[5]]=>3
[[1,5,7],[2],[3],[4],[6]]=>4
[[1,4,7],[2],[3],[5],[6]]=>5
[[1,3,7],[2],[4],[5],[6]]=>6
[[1,2,7],[3],[4],[5],[6]]=>0
[[1,5,6],[2],[3],[4],[7]]=>5
[[1,4,6],[2],[3],[5],[7]]=>6
[[1,3,6],[2],[4],[5],[7]]=>0
[[1,2,6],[3],[4],[5],[7]]=>1
[[1,4,5],[2],[3],[6],[7]]=>0
[[1,3,5],[2],[4],[6],[7]]=>1
[[1,2,5],[3],[4],[6],[7]]=>2
[[1,3,4],[2],[5],[6],[7]]=>2
[[1,2,4],[3],[5],[6],[7]]=>3
[[1,2,3],[4],[5],[6],[7]]=>4
[[1,5],[2,6],[3,7],[4]]=>3
[[1,4],[2,6],[3,7],[5]]=>6
[[1,3],[2,6],[4,7],[5]]=>0
[[1,2],[3,6],[4,7],[5]]=>1
[[1,4],[2,5],[3,7],[6]]=>5
[[1,3],[2,5],[4,7],[6]]=>2
[[1,2],[3,5],[4,7],[6]]=>3
[[1,3],[2,4],[5,7],[6]]=>6
[[1,2],[3,4],[5,7],[6]]=>4
[[1,4],[2,5],[3,6],[7]]=>4
[[1,3],[2,5],[4,6],[7]]=>1
[[1,2],[3,5],[4,6],[7]]=>2
[[1,3],[2,4],[5,6],[7]]=>0
[[1,2],[3,4],[5,6],[7]]=>5
[[1,6],[2,7],[3],[4],[5]]=>2
[[1,5],[2,7],[3],[4],[6]]=>4
[[1,4],[2,7],[3],[5],[6]]=>5
[[1,3],[2,7],[4],[5],[6]]=>6
[[1,2],[3,7],[4],[5],[6]]=>0
[[1,5],[2,6],[3],[4],[7]]=>3
[[1,4],[2,6],[3],[5],[7]]=>6
[[1,3],[2,6],[4],[5],[7]]=>0
[[1,2],[3,6],[4],[5],[7]]=>1
[[1,4],[2,5],[3],[6],[7]]=>4
[[1,3],[2,5],[4],[6],[7]]=>1
[[1,2],[3,5],[4],[6],[7]]=>2
[[1,3],[2,4],[5],[6],[7]]=>5
[[1,2],[3,4],[5],[6],[7]]=>3
[[1,7],[2],[3],[4],[5],[6]]=>1
[[1,6],[2],[3],[4],[5],[7]]=>2
[[1,5],[2],[3],[4],[6],[7]]=>3
[[1,4],[2],[3],[5],[6],[7]]=>4
[[1,3],[2],[4],[5],[6],[7]]=>5
[[1,2],[3],[4],[5],[6],[7]]=>6
[[1],[2],[3],[4],[5],[6],[7]]=>0
[[1,2,3,4,5,6,7,8]]=>0
[[1,3,4,5,6,7,8],[2]]=>1
[[1,2,4,5,6,7,8],[3]]=>2
[[1,2,3,5,6,7,8],[4]]=>3
[[1,2,3,4,6,7,8],[5]]=>4
[[1,2,3,4,5,7,8],[6]]=>5
[[1,2,3,4,5,6,8],[7]]=>6
[[1,2,3,4,5,6,7],[8]]=>7
[[1,3,5,6,7,8],[2,4]]=>4
[[1,2,5,6,7,8],[3,4]]=>2
[[1,3,4,6,7,8],[2,5]]=>5
[[1,2,4,6,7,8],[3,5]]=>6
[[1,2,3,6,7,8],[4,5]]=>3
[[1,3,4,5,7,8],[2,6]]=>6
[[1,2,4,5,7,8],[3,6]]=>7
[[1,2,3,5,7,8],[4,6]]=>0
[[1,2,3,4,7,8],[5,6]]=>4
[[1,3,4,5,6,8],[2,7]]=>7
[[1,2,4,5,6,8],[3,7]]=>0
[[1,2,3,5,6,8],[4,7]]=>1
[[1,2,3,4,6,8],[5,7]]=>2
[[1,2,3,4,5,8],[6,7]]=>5
[[1,3,4,5,6,7],[2,8]]=>0
[[1,2,4,5,6,7],[3,8]]=>1
[[1,2,3,5,6,7],[4,8]]=>2
[[1,2,3,4,6,7],[5,8]]=>3
[[1,2,3,4,5,7],[6,8]]=>4
[[1,2,3,4,5,6],[7,8]]=>6
[[1,4,5,6,7,8],[2],[3]]=>3
[[1,3,5,6,7,8],[2],[4]]=>4
[[1,2,5,6,7,8],[3],[4]]=>5
[[1,3,4,6,7,8],[2],[5]]=>5
[[1,2,4,6,7,8],[3],[5]]=>6
[[1,2,3,6,7,8],[4],[5]]=>7
[[1,3,4,5,7,8],[2],[6]]=>6
[[1,2,4,5,7,8],[3],[6]]=>7
[[1,2,3,5,7,8],[4],[6]]=>0
[[1,2,3,4,7,8],[5],[6]]=>1
[[1,3,4,5,6,8],[2],[7]]=>7
[[1,2,4,5,6,8],[3],[7]]=>0
[[1,2,3,5,6,8],[4],[7]]=>1
[[1,2,3,4,6,8],[5],[7]]=>2
[[1,2,3,4,5,8],[6],[7]]=>3
[[1,3,4,5,6,7],[2],[8]]=>0
[[1,2,4,5,6,7],[3],[8]]=>1
[[1,2,3,5,6,7],[4],[8]]=>2
[[1,2,3,4,6,7],[5],[8]]=>3
[[1,2,3,4,5,7],[6],[8]]=>4
[[1,2,3,4,5,6],[7],[8]]=>5
[[1,3,5,7,8],[2,4,6]]=>1
[[1,2,5,7,8],[3,4,6]]=>7
[[1,3,4,7,8],[2,5,6]]=>5
[[1,2,4,7,8],[3,5,6]]=>6
[[1,2,3,7,8],[4,5,6]]=>3
[[1,3,5,6,8],[2,4,7]]=>2
[[1,2,5,6,8],[3,4,7]]=>0
[[1,3,4,6,8],[2,5,7]]=>3
[[1,2,4,6,8],[3,5,7]]=>4
[[1,2,3,6,8],[4,5,7]]=>1
[[1,3,4,5,8],[2,6,7]]=>6
[[1,2,4,5,8],[3,6,7]]=>7
[[1,2,3,5,8],[4,6,7]]=>0
[[1,2,3,4,8],[5,6,7]]=>4
[[1,3,5,6,7],[2,4,8]]=>3
[[1,2,5,6,7],[3,4,8]]=>1
[[1,3,4,6,7],[2,5,8]]=>4
[[1,2,4,6,7],[3,5,8]]=>5
[[1,2,3,6,7],[4,5,8]]=>2
[[1,3,4,5,7],[2,6,8]]=>5
[[1,2,4,5,7],[3,6,8]]=>6
[[1,2,3,5,7],[4,6,8]]=>7
[[1,2,3,4,7],[5,6,8]]=>3
[[1,3,4,5,6],[2,7,8]]=>7
[[1,2,4,5,6],[3,7,8]]=>0
[[1,2,3,5,6],[4,7,8]]=>1
[[1,2,3,4,6],[5,7,8]]=>2
[[1,2,3,4,5],[6,7,8]]=>5
[[1,4,6,7,8],[2,5],[3]]=>7
[[1,3,6,7,8],[2,5],[4]]=>4
[[1,2,6,7,8],[3,5],[4]]=>5
[[1,3,6,7,8],[2,4],[5]]=>0
[[1,2,6,7,8],[3,4],[5]]=>6
[[1,4,5,7,8],[2,6],[3]]=>0
[[1,3,5,7,8],[2,6],[4]]=>1
[[1,2,5,7,8],[3,6],[4]]=>2
[[1,3,4,7,8],[2,6],[5]]=>5
[[1,2,4,7,8],[3,6],[5]]=>6
[[1,2,3,7,8],[4,6],[5]]=>7
[[1,3,5,7,8],[2,4],[6]]=>1
[[1,2,5,7,8],[3,4],[6]]=>7
[[1,3,4,7,8],[2,5],[6]]=>2
[[1,2,4,7,8],[3,5],[6]]=>3
[[1,2,3,7,8],[4,5],[6]]=>0
[[1,4,5,6,8],[2,7],[3]]=>1
[[1,3,5,6,8],[2,7],[4]]=>2
[[1,2,5,6,8],[3,7],[4]]=>3
[[1,3,4,6,8],[2,7],[5]]=>3
[[1,2,4,6,8],[3,7],[5]]=>4
[[1,2,3,6,8],[4,7],[5]]=>5
[[1,3,4,5,8],[2,7],[6]]=>6
[[1,2,4,5,8],[3,7],[6]]=>7
[[1,2,3,5,8],[4,7],[6]]=>0
[[1,2,3,4,8],[5,7],[6]]=>1
[[1,3,5,6,8],[2,4],[7]]=>2
[[1,2,5,6,8],[3,4],[7]]=>0
[[1,3,4,6,8],[2,5],[7]]=>3
[[1,2,4,6,8],[3,5],[7]]=>4
[[1,2,3,6,8],[4,5],[7]]=>1
[[1,3,4,5,8],[2,6],[7]]=>4
[[1,2,4,5,8],[3,6],[7]]=>5
[[1,2,3,5,8],[4,6],[7]]=>6
[[1,2,3,4,8],[5,6],[7]]=>2
[[1,4,5,6,7],[2,8],[3]]=>2
[[1,3,5,6,7],[2,8],[4]]=>3
[[1,2,5,6,7],[3,8],[4]]=>4
[[1,3,4,6,7],[2,8],[5]]=>4
[[1,2,4,6,7],[3,8],[5]]=>5
[[1,2,3,6,7],[4,8],[5]]=>6
[[1,3,4,5,7],[2,8],[6]]=>5
[[1,2,4,5,7],[3,8],[6]]=>6
[[1,2,3,5,7],[4,8],[6]]=>7
[[1,2,3,4,7],[5,8],[6]]=>0
[[1,3,4,5,6],[2,8],[7]]=>7
[[1,2,4,5,6],[3,8],[7]]=>0
[[1,2,3,5,6],[4,8],[7]]=>1
[[1,2,3,4,6],[5,8],[7]]=>2
[[1,2,3,4,5],[6,8],[7]]=>3
[[1,3,5,6,7],[2,4],[8]]=>3
[[1,2,5,6,7],[3,4],[8]]=>1
[[1,3,4,6,7],[2,5],[8]]=>4
[[1,2,4,6,7],[3,5],[8]]=>5
[[1,2,3,6,7],[4,5],[8]]=>2
[[1,3,4,5,7],[2,6],[8]]=>5
[[1,2,4,5,7],[3,6],[8]]=>6
[[1,2,3,5,7],[4,6],[8]]=>7
[[1,2,3,4,7],[5,6],[8]]=>3
[[1,3,4,5,6],[2,7],[8]]=>6
[[1,2,4,5,6],[3,7],[8]]=>7
[[1,2,3,5,6],[4,7],[8]]=>0
[[1,2,3,4,6],[5,7],[8]]=>1
[[1,2,3,4,5],[6,7],[8]]=>4
[[1,5,6,7,8],[2],[3],[4]]=>6
[[1,4,6,7,8],[2],[3],[5]]=>7
[[1,3,6,7,8],[2],[4],[5]]=>0
[[1,2,6,7,8],[3],[4],[5]]=>1
[[1,4,5,7,8],[2],[3],[6]]=>0
[[1,3,5,7,8],[2],[4],[6]]=>1
[[1,2,5,7,8],[3],[4],[6]]=>2
[[1,3,4,7,8],[2],[5],[6]]=>2
[[1,2,4,7,8],[3],[5],[6]]=>3
[[1,2,3,7,8],[4],[5],[6]]=>4
[[1,4,5,6,8],[2],[3],[7]]=>1
[[1,3,5,6,8],[2],[4],[7]]=>2
[[1,2,5,6,8],[3],[4],[7]]=>3
[[1,3,4,6,8],[2],[5],[7]]=>3
[[1,2,4,6,8],[3],[5],[7]]=>4
[[1,2,3,6,8],[4],[5],[7]]=>5
[[1,3,4,5,8],[2],[6],[7]]=>4
[[1,2,4,5,8],[3],[6],[7]]=>5
[[1,2,3,5,8],[4],[6],[7]]=>6
[[1,2,3,4,8],[5],[6],[7]]=>7
[[1,4,5,6,7],[2],[3],[8]]=>2
[[1,3,5,6,7],[2],[4],[8]]=>3
[[1,2,5,6,7],[3],[4],[8]]=>4
[[1,3,4,6,7],[2],[5],[8]]=>4
[[1,2,4,6,7],[3],[5],[8]]=>5
[[1,2,3,6,7],[4],[5],[8]]=>6
[[1,3,4,5,7],[2],[6],[8]]=>5
[[1,2,4,5,7],[3],[6],[8]]=>6
[[1,2,3,5,7],[4],[6],[8]]=>7
[[1,2,3,4,7],[5],[6],[8]]=>0
[[1,3,4,5,6],[2],[7],[8]]=>6
[[1,2,4,5,6],[3],[7],[8]]=>7
[[1,2,3,5,6],[4],[7],[8]]=>0
[[1,2,3,4,6],[5],[7],[8]]=>1
[[1,2,3,4,5],[6],[7],[8]]=>2
[[1,3,5,7],[2,4,6,8]]=>0
[[1,2,5,7],[3,4,6,8]]=>6
[[1,3,4,7],[2,5,6,8]]=>4
[[1,2,4,7],[3,5,6,8]]=>5
[[1,2,3,7],[4,5,6,8]]=>2
[[1,3,5,6],[2,4,7,8]]=>2
[[1,2,5,6],[3,4,7,8]]=>0
[[1,3,4,6],[2,5,7,8]]=>3
[[1,2,4,6],[3,5,7,8]]=>4
[[1,2,3,6],[4,5,7,8]]=>1
[[1,3,4,5],[2,6,7,8]]=>6
[[1,2,4,5],[3,6,7,8]]=>7
[[1,2,3,5],[4,6,7,8]]=>0
[[1,2,3,4],[5,6,7,8]]=>4
[[1,4,6,8],[2,5,7],[3]]=>5
[[1,3,6,8],[2,5,7],[4]]=>2
[[1,2,6,8],[3,5,7],[4]]=>3
[[1,3,6,8],[2,4,7],[5]]=>6
[[1,2,6,8],[3,4,7],[5]]=>4
[[1,4,5,8],[2,6,7],[3]]=>0
[[1,3,5,8],[2,6,7],[4]]=>1
[[1,2,5,8],[3,6,7],[4]]=>2
[[1,3,4,8],[2,6,7],[5]]=>5
[[1,2,4,8],[3,6,7],[5]]=>6
[[1,2,3,8],[4,6,7],[5]]=>7
[[1,3,5,8],[2,4,7],[6]]=>1
[[1,2,5,8],[3,4,7],[6]]=>7
[[1,3,4,8],[2,5,7],[6]]=>2
[[1,2,4,8],[3,5,7],[6]]=>3
[[1,2,3,8],[4,5,7],[6]]=>0
[[1,3,5,8],[2,4,6],[7]]=>7
[[1,2,5,8],[3,4,6],[7]]=>5
[[1,3,4,8],[2,5,6],[7]]=>3
[[1,2,4,8],[3,5,6],[7]]=>4
[[1,2,3,8],[4,5,6],[7]]=>1
[[1,4,6,7],[2,5,8],[3]]=>6
[[1,3,6,7],[2,5,8],[4]]=>3
[[1,2,6,7],[3,5,8],[4]]=>4
[[1,3,6,7],[2,4,8],[5]]=>7
[[1,2,6,7],[3,4,8],[5]]=>5
[[1,4,5,7],[2,6,8],[3]]=>7
[[1,3,5,7],[2,6,8],[4]]=>0
[[1,2,5,7],[3,6,8],[4]]=>1
[[1,3,4,7],[2,6,8],[5]]=>4
[[1,2,4,7],[3,6,8],[5]]=>5
[[1,2,3,7],[4,6,8],[5]]=>6
[[1,3,5,7],[2,4,8],[6]]=>0
[[1,2,5,7],[3,4,8],[6]]=>6
[[1,3,4,7],[2,5,8],[6]]=>1
[[1,2,4,7],[3,5,8],[6]]=>2
[[1,2,3,7],[4,5,8],[6]]=>7
[[1,4,5,6],[2,7,8],[3]]=>1
[[1,3,5,6],[2,7,8],[4]]=>2
[[1,2,5,6],[3,7,8],[4]]=>3
[[1,3,4,6],[2,7,8],[5]]=>3
[[1,2,4,6],[3,7,8],[5]]=>4
[[1,2,3,6],[4,7,8],[5]]=>5
[[1,3,4,5],[2,7,8],[6]]=>6
[[1,2,4,5],[3,7,8],[6]]=>7
[[1,2,3,5],[4,7,8],[6]]=>0
[[1,2,3,4],[5,7,8],[6]]=>1
[[1,3,5,6],[2,4,8],[7]]=>2
[[1,2,5,6],[3,4,8],[7]]=>0
[[1,3,4,6],[2,5,8],[7]]=>3
[[1,2,4,6],[3,5,8],[7]]=>4
[[1,2,3,6],[4,5,8],[7]]=>1
[[1,3,4,5],[2,6,8],[7]]=>4
[[1,2,4,5],[3,6,8],[7]]=>5
[[1,2,3,5],[4,6,8],[7]]=>6
[[1,2,3,4],[5,6,8],[7]]=>2
[[1,3,5,7],[2,4,6],[8]]=>0
[[1,2,5,7],[3,4,6],[8]]=>6
[[1,3,4,7],[2,5,6],[8]]=>4
[[1,2,4,7],[3,5,6],[8]]=>5
[[1,2,3,7],[4,5,6],[8]]=>2
[[1,3,5,6],[2,4,7],[8]]=>1
[[1,2,5,6],[3,4,7],[8]]=>7
[[1,3,4,6],[2,5,7],[8]]=>2
[[1,2,4,6],[3,5,7],[8]]=>3
[[1,2,3,6],[4,5,7],[8]]=>0
[[1,3,4,5],[2,6,7],[8]]=>5
[[1,2,4,5],[3,6,7],[8]]=>6
[[1,2,3,5],[4,6,7],[8]]=>7
[[1,2,3,4],[5,6,7],[8]]=>3
[[1,4,7,8],[2,5],[3,6]]=>4
[[1,3,7,8],[2,5],[4,6]]=>1
[[1,2,7,8],[3,5],[4,6]]=>2
[[1,3,7,8],[2,4],[5,6]]=>0
[[1,2,7,8],[3,4],[5,6]]=>6
[[1,4,6,8],[2,5],[3,7]]=>5
[[1,3,6,8],[2,5],[4,7]]=>2
[[1,2,6,8],[3,5],[4,7]]=>3
[[1,3,6,8],[2,4],[5,7]]=>6
[[1,2,6,8],[3,4],[5,7]]=>4
[[1,4,5,8],[2,6],[3,7]]=>6
[[1,3,5,8],[2,6],[4,7]]=>7
[[1,2,5,8],[3,6],[4,7]]=>0
[[1,3,4,8],[2,6],[5,7]]=>3
[[1,2,4,8],[3,6],[5,7]]=>4
[[1,2,3,8],[4,6],[5,7]]=>5
[[1,3,5,8],[2,4],[6,7]]=>1
[[1,2,5,8],[3,4],[6,7]]=>7
[[1,3,4,8],[2,5],[6,7]]=>2
[[1,2,4,8],[3,5],[6,7]]=>3
[[1,2,3,8],[4,5],[6,7]]=>0
[[1,4,6,7],[2,5],[3,8]]=>6
[[1,3,6,7],[2,5],[4,8]]=>3
[[1,2,6,7],[3,5],[4,8]]=>4
[[1,3,6,7],[2,4],[5,8]]=>7
[[1,2,6,7],[3,4],[5,8]]=>5
[[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]]=>1
[[1,3,4,7],[2,6],[5,8]]=>4
[[1,2,4,7],[3,6],[5,8]]=>5
[[1,2,3,7],[4,6],[5,8]]=>6
[[1,3,5,7],[2,4],[6,8]]=>0
[[1,2,5,7],[3,4],[6,8]]=>6
[[1,3,4,7],[2,5],[6,8]]=>1
[[1,2,4,7],[3,5],[6,8]]=>2
[[1,2,3,7],[4,5],[6,8]]=>7
[[1,4,5,6],[2,7],[3,8]]=>0
[[1,3,5,6],[2,7],[4,8]]=>1
[[1,2,5,6],[3,7],[4,8]]=>2
[[1,3,4,6],[2,7],[5,8]]=>2
[[1,2,4,6],[3,7],[5,8]]=>3
[[1,2,3,6],[4,7],[5,8]]=>4
[[1,3,4,5],[2,7],[6,8]]=>5
[[1,2,4,5],[3,7],[6,8]]=>6
[[1,2,3,5],[4,7],[6,8]]=>7
[[1,2,3,4],[5,7],[6,8]]=>0
[[1,3,5,6],[2,4],[7,8]]=>2
[[1,2,5,6],[3,4],[7,8]]=>0
[[1,3,4,6],[2,5],[7,8]]=>3
[[1,2,4,6],[3,5],[7,8]]=>4
[[1,2,3,6],[4,5],[7,8]]=>1
[[1,3,4,5],[2,6],[7,8]]=>4
[[1,2,4,5],[3,6],[7,8]]=>5
[[1,2,3,5],[4,6],[7,8]]=>6
[[1,2,3,4],[5,6],[7,8]]=>2
[[1,5,7,8],[2,6],[3],[4]]=>3
[[1,4,7,8],[2,6],[3],[5]]=>7
[[1,3,7,8],[2,6],[4],[5]]=>0
[[1,2,7,8],[3,6],[4],[5]]=>1
[[1,4,7,8],[2,5],[3],[6]]=>4
[[1,3,7,8],[2,5],[4],[6]]=>1
[[1,2,7,8],[3,5],[4],[6]]=>2
[[1,3,7,8],[2,4],[5],[6]]=>5
[[1,2,7,8],[3,4],[5],[6]]=>3
[[1,5,6,8],[2,7],[3],[4]]=>4
[[1,4,6,8],[2,7],[3],[5]]=>5
[[1,3,6,8],[2,7],[4],[5]]=>6
[[1,2,6,8],[3,7],[4],[5]]=>7
[[1,4,5,8],[2,7],[3],[6]]=>0
[[1,3,5,8],[2,7],[4],[6]]=>1
[[1,2,5,8],[3,7],[4],[6]]=>2
[[1,3,4,8],[2,7],[5],[6]]=>2
[[1,2,4,8],[3,7],[5],[6]]=>3
[[1,2,3,8],[4,7],[5],[6]]=>4
[[1,4,6,8],[2,5],[3],[7]]=>5
[[1,3,6,8],[2,5],[4],[7]]=>2
[[1,2,6,8],[3,5],[4],[7]]=>3
[[1,3,6,8],[2,4],[5],[7]]=>6
[[1,2,6,8],[3,4],[5],[7]]=>4
[[1,4,5,8],[2,6],[3],[7]]=>6
[[1,3,5,8],[2,6],[4],[7]]=>7
[[1,2,5,8],[3,6],[4],[7]]=>0
[[1,3,4,8],[2,6],[5],[7]]=>3
[[1,2,4,8],[3,6],[5],[7]]=>4
[[1,2,3,8],[4,6],[5],[7]]=>5
[[1,3,5,8],[2,4],[6],[7]]=>7
[[1,2,5,8],[3,4],[6],[7]]=>5
[[1,3,4,8],[2,5],[6],[7]]=>0
[[1,2,4,8],[3,5],[6],[7]]=>1
[[1,2,3,8],[4,5],[6],[7]]=>6
[[1,5,6,7],[2,8],[3],[4]]=>5
[[1,4,6,7],[2,8],[3],[5]]=>6
[[1,3,6,7],[2,8],[4],[5]]=>7
[[1,2,6,7],[3,8],[4],[5]]=>0
[[1,4,5,7],[2,8],[3],[6]]=>7
[[1,3,5,7],[2,8],[4],[6]]=>0
[[1,2,5,7],[3,8],[4],[6]]=>1
[[1,3,4,7],[2,8],[5],[6]]=>1
[[1,2,4,7],[3,8],[5],[6]]=>2
[[1,2,3,7],[4,8],[5],[6]]=>3
[[1,4,5,6],[2,8],[3],[7]]=>1
[[1,3,5,6],[2,8],[4],[7]]=>2
[[1,2,5,6],[3,8],[4],[7]]=>3
[[1,3,4,6],[2,8],[5],[7]]=>3
[[1,2,4,6],[3,8],[5],[7]]=>4
[[1,2,3,6],[4,8],[5],[7]]=>5
[[1,3,4,5],[2,8],[6],[7]]=>4
[[1,2,4,5],[3,8],[6],[7]]=>5
[[1,2,3,5],[4,8],[6],[7]]=>6
[[1,2,3,4],[5,8],[6],[7]]=>7
[[1,4,6,7],[2,5],[3],[8]]=>6
[[1,3,6,7],[2,5],[4],[8]]=>3
[[1,2,6,7],[3,5],[4],[8]]=>4
[[1,3,6,7],[2,4],[5],[8]]=>7
[[1,2,6,7],[3,4],[5],[8]]=>5
[[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]]=>1
[[1,3,4,7],[2,6],[5],[8]]=>4
[[1,2,4,7],[3,6],[5],[8]]=>5
[[1,2,3,7],[4,6],[5],[8]]=>6
[[1,3,5,7],[2,4],[6],[8]]=>0
[[1,2,5,7],[3,4],[6],[8]]=>6
[[1,3,4,7],[2,5],[6],[8]]=>1
[[1,2,4,7],[3,5],[6],[8]]=>2
[[1,2,3,7],[4,5],[6],[8]]=>7
[[1,4,5,6],[2,7],[3],[8]]=>0
[[1,3,5,6],[2,7],[4],[8]]=>1
[[1,2,5,6],[3,7],[4],[8]]=>2
[[1,3,4,6],[2,7],[5],[8]]=>2
[[1,2,4,6],[3,7],[5],[8]]=>3
[[1,2,3,6],[4,7],[5],[8]]=>4
[[1,3,4,5],[2,7],[6],[8]]=>5
[[1,2,4,5],[3,7],[6],[8]]=>6
[[1,2,3,5],[4,7],[6],[8]]=>7
[[1,2,3,4],[5,7],[6],[8]]=>0
[[1,3,5,6],[2,4],[7],[8]]=>1
[[1,2,5,6],[3,4],[7],[8]]=>7
[[1,3,4,6],[2,5],[7],[8]]=>2
[[1,2,4,6],[3,5],[7],[8]]=>3
[[1,2,3,6],[4,5],[7],[8]]=>0
[[1,3,4,5],[2,6],[7],[8]]=>3
[[1,2,4,5],[3,6],[7],[8]]=>4
[[1,2,3,5],[4,6],[7],[8]]=>5
[[1,2,3,4],[5,6],[7],[8]]=>1
[[1,6,7,8],[2],[3],[4],[5]]=>2
[[1,5,7,8],[2],[3],[4],[6]]=>3
[[1,4,7,8],[2],[3],[5],[6]]=>4
[[1,3,7,8],[2],[4],[5],[6]]=>5
[[1,2,7,8],[3],[4],[5],[6]]=>6
[[1,5,6,8],[2],[3],[4],[7]]=>4
[[1,4,6,8],[2],[3],[5],[7]]=>5
[[1,3,6,8],[2],[4],[5],[7]]=>6
[[1,2,6,8],[3],[4],[5],[7]]=>7
[[1,4,5,8],[2],[3],[6],[7]]=>6
[[1,3,5,8],[2],[4],[6],[7]]=>7
[[1,2,5,8],[3],[4],[6],[7]]=>0
[[1,3,4,8],[2],[5],[6],[7]]=>0
[[1,2,4,8],[3],[5],[6],[7]]=>1
[[1,2,3,8],[4],[5],[6],[7]]=>2
[[1,5,6,7],[2],[3],[4],[8]]=>5
[[1,4,6,7],[2],[3],[5],[8]]=>6
[[1,3,6,7],[2],[4],[5],[8]]=>7
[[1,2,6,7],[3],[4],[5],[8]]=>0
[[1,4,5,7],[2],[3],[6],[8]]=>7
[[1,3,5,7],[2],[4],[6],[8]]=>0
[[1,2,5,7],[3],[4],[6],[8]]=>1
[[1,3,4,7],[2],[5],[6],[8]]=>1
[[1,2,4,7],[3],[5],[6],[8]]=>2
[[1,2,3,7],[4],[5],[6],[8]]=>3
[[1,4,5,6],[2],[3],[7],[8]]=>0
[[1,3,5,6],[2],[4],[7],[8]]=>1
[[1,2,5,6],[3],[4],[7],[8]]=>2
[[1,3,4,6],[2],[5],[7],[8]]=>2
[[1,2,4,6],[3],[5],[7],[8]]=>3
[[1,2,3,6],[4],[5],[7],[8]]=>4
[[1,3,4,5],[2],[6],[7],[8]]=>3
[[1,2,4,5],[3],[6],[7],[8]]=>4
[[1,2,3,5],[4],[6],[7],[8]]=>5
[[1,2,3,4],[5],[6],[7],[8]]=>6
[[1,4,7],[2,5,8],[3,6]]=>3
[[1,3,7],[2,5,8],[4,6]]=>0
[[1,2,7],[3,5,8],[4,6]]=>1
[[1,3,7],[2,4,8],[5,6]]=>7
[[1,2,7],[3,4,8],[5,6]]=>5
[[1,4,6],[2,5,8],[3,7]]=>5
[[1,3,6],[2,5,8],[4,7]]=>2
[[1,2,6],[3,5,8],[4,7]]=>3
[[1,3,6],[2,4,8],[5,7]]=>6
[[1,2,6],[3,4,8],[5,7]]=>4
[[1,4,5],[2,6,8],[3,7]]=>6
[[1,3,5],[2,6,8],[4,7]]=>7
[[1,2,5],[3,6,8],[4,7]]=>0
[[1,3,4],[2,6,8],[5,7]]=>3
[[1,2,4],[3,6,8],[5,7]]=>4
[[1,2,3],[4,6,8],[5,7]]=>5
[[1,3,5],[2,4,8],[6,7]]=>1
[[1,2,5],[3,4,8],[6,7]]=>7
[[1,3,4],[2,5,8],[6,7]]=>2
[[1,2,4],[3,5,8],[6,7]]=>3
[[1,2,3],[4,5,8],[6,7]]=>0
[[1,4,6],[2,5,7],[3,8]]=>4
[[1,3,6],[2,5,7],[4,8]]=>1
[[1,2,6],[3,5,7],[4,8]]=>2
[[1,3,6],[2,4,7],[5,8]]=>5
[[1,2,6],[3,4,7],[5,8]]=>3
[[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]]=>1
[[1,3,4],[2,6,7],[5,8]]=>4
[[1,2,4],[3,6,7],[5,8]]=>5
[[1,2,3],[4,6,7],[5,8]]=>6
[[1,3,5],[2,4,7],[6,8]]=>0
[[1,2,5],[3,4,7],[6,8]]=>6
[[1,3,4],[2,5,7],[6,8]]=>1
[[1,2,4],[3,5,7],[6,8]]=>2
[[1,2,3],[4,5,7],[6,8]]=>7
[[1,3,5],[2,4,6],[7,8]]=>7
[[1,2,5],[3,4,6],[7,8]]=>5
[[1,3,4],[2,5,6],[7,8]]=>3
[[1,2,4],[3,5,6],[7,8]]=>4
[[1,2,3],[4,5,6],[7,8]]=>1
[[1,5,7],[2,6,8],[3],[4]]=>2
[[1,4,7],[2,6,8],[3],[5]]=>6
[[1,3,7],[2,6,8],[4],[5]]=>7
[[1,2,7],[3,6,8],[4],[5]]=>0
[[1,4,7],[2,5,8],[3],[6]]=>3
[[1,3,7],[2,5,8],[4],[6]]=>0
[[1,2,7],[3,5,8],[4],[6]]=>1
[[1,3,7],[2,4,8],[5],[6]]=>4
[[1,2,7],[3,4,8],[5],[6]]=>2
[[1,5,6],[2,7,8],[3],[4]]=>4
[[1,4,6],[2,7,8],[3],[5]]=>5
[[1,3,6],[2,7,8],[4],[5]]=>6
[[1,2,6],[3,7,8],[4],[5]]=>7
[[1,4,5],[2,7,8],[3],[6]]=>0
[[1,3,5],[2,7,8],[4],[6]]=>1
[[1,2,5],[3,7,8],[4],[6]]=>2
[[1,3,4],[2,7,8],[5],[6]]=>2
[[1,2,4],[3,7,8],[5],[6]]=>3
[[1,2,3],[4,7,8],[5],[6]]=>4
[[1,4,6],[2,5,8],[3],[7]]=>5
[[1,3,6],[2,5,8],[4],[7]]=>2
[[1,2,6],[3,5,8],[4],[7]]=>3
[[1,3,6],[2,4,8],[5],[7]]=>6
[[1,2,6],[3,4,8],[5],[7]]=>4
[[1,4,5],[2,6,8],[3],[7]]=>6
[[1,3,5],[2,6,8],[4],[7]]=>7
[[1,2,5],[3,6,8],[4],[7]]=>0
[[1,3,4],[2,6,8],[5],[7]]=>3
[[1,2,4],[3,6,8],[5],[7]]=>4
[[1,2,3],[4,6,8],[5],[7]]=>5
[[1,3,5],[2,4,8],[6],[7]]=>7
[[1,2,5],[3,4,8],[6],[7]]=>5
[[1,3,4],[2,5,8],[6],[7]]=>0
[[1,2,4],[3,5,8],[6],[7]]=>1
[[1,2,3],[4,5,8],[6],[7]]=>6
[[1,4,6],[2,5,7],[3],[8]]=>4
[[1,3,6],[2,5,7],[4],[8]]=>1
[[1,2,6],[3,5,7],[4],[8]]=>2
[[1,3,6],[2,4,7],[5],[8]]=>5
[[1,2,6],[3,4,7],[5],[8]]=>3
[[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]]=>1
[[1,3,4],[2,6,7],[5],[8]]=>4
[[1,2,4],[3,6,7],[5],[8]]=>5
[[1,2,3],[4,6,7],[5],[8]]=>6
[[1,3,5],[2,4,7],[6],[8]]=>0
[[1,2,5],[3,4,7],[6],[8]]=>6
[[1,3,4],[2,5,7],[6],[8]]=>1
[[1,2,4],[3,5,7],[6],[8]]=>2
[[1,2,3],[4,5,7],[6],[8]]=>7
[[1,3,5],[2,4,6],[7],[8]]=>6
[[1,2,5],[3,4,6],[7],[8]]=>4
[[1,3,4],[2,5,6],[7],[8]]=>2
[[1,2,4],[3,5,6],[7],[8]]=>3
[[1,2,3],[4,5,6],[7],[8]]=>0
[[1,5,8],[2,6],[3,7],[4]]=>1
[[1,4,8],[2,6],[3,7],[5]]=>5
[[1,3,8],[2,6],[4,7],[5]]=>6
[[1,2,8],[3,6],[4,7],[5]]=>7
[[1,4,8],[2,5],[3,7],[6]]=>4
[[1,3,8],[2,5],[4,7],[6]]=>1
[[1,2,8],[3,5],[4,7],[6]]=>2
[[1,3,8],[2,4],[5,7],[6]]=>5
[[1,2,8],[3,4],[5,7],[6]]=>3
[[1,4,8],[2,5],[3,6],[7]]=>2
[[1,3,8],[2,5],[4,6],[7]]=>7
[[1,2,8],[3,5],[4,6],[7]]=>0
[[1,3,8],[2,4],[5,6],[7]]=>6
[[1,2,8],[3,4],[5,6],[7]]=>4
[[1,5,7],[2,6],[3,8],[4]]=>2
[[1,4,7],[2,6],[3,8],[5]]=>6
[[1,3,7],[2,6],[4,8],[5]]=>7
[[1,2,7],[3,6],[4,8],[5]]=>0
[[1,4,7],[2,5],[3,8],[6]]=>3
[[1,3,7],[2,5],[4,8],[6]]=>0
[[1,2,7],[3,5],[4,8],[6]]=>1
[[1,3,7],[2,4],[5,8],[6]]=>4
[[1,2,7],[3,4],[5,8],[6]]=>2
[[1,5,6],[2,7],[3,8],[4]]=>3
[[1,4,6],[2,7],[3,8],[5]]=>4
[[1,3,6],[2,7],[4,8],[5]]=>5
[[1,2,6],[3,7],[4,8],[5]]=>6
[[1,4,5],[2,7],[3,8],[6]]=>7
[[1,3,5],[2,7],[4,8],[6]]=>0
[[1,2,5],[3,7],[4,8],[6]]=>1
[[1,3,4],[2,7],[5,8],[6]]=>1
[[1,2,4],[3,7],[5,8],[6]]=>2
[[1,2,3],[4,7],[5,8],[6]]=>3
[[1,4,6],[2,5],[3,8],[7]]=>5
[[1,3,6],[2,5],[4,8],[7]]=>2
[[1,2,6],[3,5],[4,8],[7]]=>3
[[1,3,6],[2,4],[5,8],[7]]=>6
[[1,2,6],[3,4],[5,8],[7]]=>4
[[1,4,5],[2,6],[3,8],[7]]=>6
[[1,3,5],[2,6],[4,8],[7]]=>7
[[1,2,5],[3,6],[4,8],[7]]=>0
[[1,3,4],[2,6],[5,8],[7]]=>3
[[1,2,4],[3,6],[5,8],[7]]=>4
[[1,2,3],[4,6],[5,8],[7]]=>5
[[1,3,5],[2,4],[6,8],[7]]=>7
[[1,2,5],[3,4],[6,8],[7]]=>5
[[1,3,4],[2,5],[6,8],[7]]=>0
[[1,2,4],[3,5],[6,8],[7]]=>1
[[1,2,3],[4,5],[6,8],[7]]=>6
[[1,4,7],[2,5],[3,6],[8]]=>3
[[1,3,7],[2,5],[4,6],[8]]=>0
[[1,2,7],[3,5],[4,6],[8]]=>1
[[1,3,7],[2,4],[5,6],[8]]=>7
[[1,2,7],[3,4],[5,6],[8]]=>5
[[1,4,6],[2,5],[3,7],[8]]=>4
[[1,3,6],[2,5],[4,7],[8]]=>1
[[1,2,6],[3,5],[4,7],[8]]=>2
[[1,3,6],[2,4],[5,7],[8]]=>5
[[1,2,6],[3,4],[5,7],[8]]=>3
[[1,4,5],[2,6],[3,7],[8]]=>5
[[1,3,5],[2,6],[4,7],[8]]=>6
[[1,2,5],[3,6],[4,7],[8]]=>7
[[1,3,4],[2,6],[5,7],[8]]=>2
[[1,2,4],[3,6],[5,7],[8]]=>3
[[1,2,3],[4,6],[5,7],[8]]=>4
[[1,3,5],[2,4],[6,7],[8]]=>0
[[1,2,5],[3,4],[6,7],[8]]=>6
[[1,3,4],[2,5],[6,7],[8]]=>1
[[1,2,4],[3,5],[6,7],[8]]=>2
[[1,2,3],[4,5],[6,7],[8]]=>7
[[1,6,8],[2,7],[3],[4],[5]]=>0
[[1,5,8],[2,7],[3],[4],[6]]=>3
[[1,4,8],[2,7],[3],[5],[6]]=>4
[[1,3,8],[2,7],[4],[5],[6]]=>5
[[1,2,8],[3,7],[4],[5],[6]]=>6
[[1,5,8],[2,6],[3],[4],[7]]=>1
[[1,4,8],[2,6],[3],[5],[7]]=>5
[[1,3,8],[2,6],[4],[5],[7]]=>6
[[1,2,8],[3,6],[4],[5],[7]]=>7
[[1,4,8],[2,5],[3],[6],[7]]=>2
[[1,3,8],[2,5],[4],[6],[7]]=>7
[[1,2,8],[3,5],[4],[6],[7]]=>0
[[1,3,8],[2,4],[5],[6],[7]]=>3
[[1,2,8],[3,4],[5],[6],[7]]=>1
[[1,6,7],[2,8],[3],[4],[5]]=>1
[[1,5,7],[2,8],[3],[4],[6]]=>2
[[1,4,7],[2,8],[3],[5],[6]]=>3
[[1,3,7],[2,8],[4],[5],[6]]=>4
[[1,2,7],[3,8],[4],[5],[6]]=>5
[[1,5,6],[2,8],[3],[4],[7]]=>4
[[1,4,6],[2,8],[3],[5],[7]]=>5
[[1,3,6],[2,8],[4],[5],[7]]=>6
[[1,2,6],[3,8],[4],[5],[7]]=>7
[[1,4,5],[2,8],[3],[6],[7]]=>6
[[1,3,5],[2,8],[4],[6],[7]]=>7
[[1,2,5],[3,8],[4],[6],[7]]=>0
[[1,3,4],[2,8],[5],[6],[7]]=>0
[[1,2,4],[3,8],[5],[6],[7]]=>1
[[1,2,3],[4,8],[5],[6],[7]]=>2
[[1,5,7],[2,6],[3],[4],[8]]=>2
[[1,4,7],[2,6],[3],[5],[8]]=>6
[[1,3,7],[2,6],[4],[5],[8]]=>7
[[1,2,7],[3,6],[4],[5],[8]]=>0
[[1,4,7],[2,5],[3],[6],[8]]=>3
[[1,3,7],[2,5],[4],[6],[8]]=>0
[[1,2,7],[3,5],[4],[6],[8]]=>1
[[1,3,7],[2,4],[5],[6],[8]]=>4
[[1,2,7],[3,4],[5],[6],[8]]=>2
[[1,5,6],[2,7],[3],[4],[8]]=>3
[[1,4,6],[2,7],[3],[5],[8]]=>4
[[1,3,6],[2,7],[4],[5],[8]]=>5
[[1,2,6],[3,7],[4],[5],[8]]=>6
[[1,4,5],[2,7],[3],[6],[8]]=>7
[[1,3,5],[2,7],[4],[6],[8]]=>0
[[1,2,5],[3,7],[4],[6],[8]]=>1
[[1,3,4],[2,7],[5],[6],[8]]=>1
[[1,2,4],[3,7],[5],[6],[8]]=>2
[[1,2,3],[4,7],[5],[6],[8]]=>3
[[1,4,6],[2,5],[3],[7],[8]]=>4
[[1,3,6],[2,5],[4],[7],[8]]=>1
[[1,2,6],[3,5],[4],[7],[8]]=>2
[[1,3,6],[2,4],[5],[7],[8]]=>5
[[1,2,6],[3,4],[5],[7],[8]]=>3
[[1,4,5],[2,6],[3],[7],[8]]=>5
[[1,3,5],[2,6],[4],[7],[8]]=>6
[[1,2,5],[3,6],[4],[7],[8]]=>7
[[1,3,4],[2,6],[5],[7],[8]]=>2
[[1,2,4],[3,6],[5],[7],[8]]=>3
[[1,2,3],[4,6],[5],[7],[8]]=>4
[[1,3,5],[2,4],[6],[7],[8]]=>6
[[1,2,5],[3,4],[6],[7],[8]]=>4
[[1,3,4],[2,5],[6],[7],[8]]=>7
[[1,2,4],[3,5],[6],[7],[8]]=>0
[[1,2,3],[4,5],[6],[7],[8]]=>5
[[1,7,8],[2],[3],[4],[5],[6]]=>7
[[1,6,8],[2],[3],[4],[5],[7]]=>0
[[1,5,8],[2],[3],[4],[6],[7]]=>1
[[1,4,8],[2],[3],[5],[6],[7]]=>2
[[1,3,8],[2],[4],[5],[6],[7]]=>3
[[1,2,8],[3],[4],[5],[6],[7]]=>4
[[1,6,7],[2],[3],[4],[5],[8]]=>1
[[1,5,7],[2],[3],[4],[6],[8]]=>2
[[1,4,7],[2],[3],[5],[6],[8]]=>3
[[1,3,7],[2],[4],[5],[6],[8]]=>4
[[1,2,7],[3],[4],[5],[6],[8]]=>5
[[1,5,6],[2],[3],[4],[7],[8]]=>3
[[1,4,6],[2],[3],[5],[7],[8]]=>4
[[1,3,6],[2],[4],[5],[7],[8]]=>5
[[1,2,6],[3],[4],[5],[7],[8]]=>6
[[1,4,5],[2],[3],[6],[7],[8]]=>5
[[1,3,5],[2],[4],[6],[7],[8]]=>6
[[1,2,5],[3],[4],[6],[7],[8]]=>7
[[1,3,4],[2],[5],[6],[7],[8]]=>7
[[1,2,4],[3],[5],[6],[7],[8]]=>0
[[1,2,3],[4],[5],[6],[7],[8]]=>1
[[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]]=>5
[[1,2],[3,6],[4,7],[5,8]]=>6
[[1,4],[2,5],[3,7],[6,8]]=>3
[[1,3],[2,5],[4,7],[6,8]]=>0
[[1,2],[3,5],[4,7],[6,8]]=>1
[[1,3],[2,4],[5,7],[6,8]]=>4
[[1,2],[3,4],[5,7],[6,8]]=>2
[[1,4],[2,5],[3,6],[7,8]]=>2
[[1,3],[2,5],[4,6],[7,8]]=>7
[[1,2],[3,5],[4,6],[7,8]]=>0
[[1,3],[2,4],[5,6],[7,8]]=>6
[[1,2],[3,4],[5,6],[7,8]]=>4
[[1,6],[2,7],[3,8],[4],[5]]=>7
[[1,5],[2,7],[3,8],[4],[6]]=>2
[[1,4],[2,7],[3,8],[5],[6]]=>3
[[1,3],[2,7],[4,8],[5],[6]]=>4
[[1,2],[3,7],[4,8],[5],[6]]=>5
[[1,5],[2,6],[3,8],[4],[7]]=>1
[[1,4],[2,6],[3,8],[5],[7]]=>5
[[1,3],[2,6],[4,8],[5],[7]]=>6
[[1,2],[3,6],[4,8],[5],[7]]=>7
[[1,4],[2,5],[3,8],[6],[7]]=>2
[[1,3],[2,5],[4,8],[6],[7]]=>7
[[1,2],[3,5],[4,8],[6],[7]]=>0
[[1,3],[2,4],[5,8],[6],[7]]=>3
[[1,2],[3,4],[5,8],[6],[7]]=>1
[[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]]=>5
[[1,2],[3,6],[4,7],[5],[8]]=>6
[[1,4],[2,5],[3,7],[6],[8]]=>3
[[1,3],[2,5],[4,7],[6],[8]]=>0
[[1,2],[3,5],[4,7],[6],[8]]=>1
[[1,3],[2,4],[5,7],[6],[8]]=>4
[[1,2],[3,4],[5,7],[6],[8]]=>2
[[1,4],[2,5],[3,6],[7],[8]]=>1
[[1,3],[2,5],[4,6],[7],[8]]=>6
[[1,2],[3,5],[4,6],[7],[8]]=>7
[[1,3],[2,4],[5,6],[7],[8]]=>5
[[1,2],[3,4],[5,6],[7],[8]]=>3
[[1,7],[2,8],[3],[4],[5],[6]]=>6
[[1,6],[2,8],[3],[4],[5],[7]]=>0
[[1,5],[2,8],[3],[4],[6],[7]]=>1
[[1,4],[2,8],[3],[5],[6],[7]]=>2
[[1,3],[2,8],[4],[5],[6],[7]]=>3
[[1,2],[3,8],[4],[5],[6],[7]]=>4
[[1,6],[2,7],[3],[4],[5],[8]]=>7
[[1,5],[2,7],[3],[4],[6],[8]]=>2
[[1,4],[2,7],[3],[5],[6],[8]]=>3
[[1,3],[2,7],[4],[5],[6],[8]]=>4
[[1,2],[3,7],[4],[5],[6],[8]]=>5
[[1,5],[2,6],[3],[4],[7],[8]]=>0
[[1,4],[2,6],[3],[5],[7],[8]]=>4
[[1,3],[2,6],[4],[5],[7],[8]]=>5
[[1,2],[3,6],[4],[5],[7],[8]]=>6
[[1,4],[2,5],[3],[6],[7],[8]]=>1
[[1,3],[2,5],[4],[6],[7],[8]]=>6
[[1,2],[3,5],[4],[6],[7],[8]]=>7
[[1,3],[2,4],[5],[6],[7],[8]]=>2
[[1,2],[3,4],[5],[6],[7],[8]]=>0
[[1,8],[2],[3],[4],[5],[6],[7]]=>5
[[1,7],[2],[3],[4],[5],[6],[8]]=>6
[[1,6],[2],[3],[4],[5],[7],[8]]=>7
[[1,5],[2],[3],[4],[6],[7],[8]]=>0
[[1,4],[2],[3],[5],[6],[7],[8]]=>1
[[1,3],[2],[4],[5],[6],[7],[8]]=>2
[[1,2],[3],[4],[5],[6],[7],[8]]=>3
[[1],[2],[3],[4],[5],[6],[7],[8]]=>4
[[1,2,3,4,5,6,7,8,9]]=>0
[[1,2,3,4,5,6,7,8],[9]]=>8
[[1,2,3,4,5,6,7],[8,9]]=>7
[[1,2,3,4,5,6,7],[8],[9]]=>6
[[1,3,4,5,6,7,8,9],[2]]=>1
[[1,2,5,6,7,8,9],[3,4]]=>2
[[1,4,5,6,7,8,9],[2],[3]]=>3
[[1,2,3,7,8,9],[4,5,6]]=>3
[[1,3,5,7,8,9],[2,4,6]]=>0
[[1,3,5,6,7,8,9],[2,4]]=>4
[[1,2,3,4,5,6,8],[7,9]]=>5
[[1,2,3,4,5,6,7,9],[8]]=>7
[[1,2,3,4,5,6,9],[7,8]]=>6
[[1,2,3,4,5,6,9],[7],[8]]=>4
[[1,2,4,5,6,7,8,9],[3]]=>2
[[1,3,4,6,7,8,9],[2,5]]=>5
[[1,3,5,6,7,8,9],[2],[4]]=>4
[[1,3,5,6,8,9],[2,4,7]]=>1
[[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]]=>3
[[1,2,5,6,7,8,9],[3],[4]]=>5
[[1,2,3,4,8,9],[5,6,7]]=>4
[[1,2,3,4,7,8,9],[5,6]]=>4
[[1,2,3,4,5,6,8],[7],[9]]=>5
[[1,2,3,5,7,9],[4,6,8]]=>6
[[1,2,3,4,5,7,9],[6,8]]=>3
[[1,2,4,6,8,9],[3,5,7]]=>3
[[1,2,4,6,7,8,9],[3,5]]=>6
[[1,2,4,5,6,7,8],[3,9]]=>1
[[1,3,4,5,7,9],[2,6,8]]=>4
[[1,3,4,5,6,7,9],[2,8]]=>8
[[1,2,3,5,6,7,8,9],[4]]=>3
[[1,2,4,5,7,8,9],[3,6]]=>7
[[1,2,4,6,7,8,9],[3],[5]]=>6
[[1,2,4,6,7,9],[3,5,8]]=>4
[[1,2,3,5,6,7,8],[4,9]]=>2
[[1,2,4,5,6,7,8],[3],[9]]=>1
[[1,2,3,4,5,6,8,9],[7]]=>6
[[1,2,3,4,5,7,8,9],[6]]=>5
[[1,2,3,4,6,7,8,9],[5]]=>4
[[1,2,3,4,5,8,9],[6,7]]=>5
[[1,2,3,4,5,8,9],[6],[7]]=>2
[[1,2,3,4,7,8,9],[5],[6]]=>0
[[1,2,3,6,7,8,9],[4],[5]]=>7
[[1,3,4,7,8,9],[2,5,6]]=>5
[[1,3,4,5,7,8,9],[2,6]]=>6
[[1,3,4,6,7,8,9],[2],[5]]=>5
[[1,3,5,6,7,9],[2,4,8]]=>2
[[1,2,3,4,5,7,8],[6],[9]]=>4
[[1,2,3,4,6,7,8],[5],[9]]=>3
[[1,2,3,5,6,7,8],[4],[9]]=>2
[[1,2,3,4,5,7,8],[6,9]]=>4
[[1,3,4,5,6,8,9],[2,7]]=>7
[[1,2,3,4,6,7,8],[5,9]]=>3
[[1,2,5,7,8,9],[3,4,6]]=>7
[[1,3,4,5,6,7,9],[2],[8]]=>8
[[1,3,4,5,6,8,9],[2],[7]]=>7
[[1,3,4,5,8,9],[2,6,7]]=>6
[[1,2,3,5,7,8,9],[4,6]]=>8
[[1,3,4,5,7,8,9],[2],[6]]=>6
[[1,2,3,6,8,9],[4,5,7]]=>0
[[1,2,3,4,6,8,9],[5,7]]=>1
[[1,2,4,7,8,9],[3,5,6]]=>6
[[1,2,3,4,5,7,9],[6],[8]]=>3
[[1,2,3,5,8,9],[4,6,7]]=>8
[[1,2,4,5,6,7,9],[3],[8]]=>0
[[1,2,3,4,6,8,9],[5],[7]]=>1
[[1,2,5,6,8,9],[3,4,7]]=>8
[[1,2,5,6,7,9],[3,4,8]]=>0
[[1,2,3,4,6,7,9],[5],[8]]=>2
[[1,2,3,5,6,7,9],[4,8]]=>1
[[1,2,3,5,6,8,9],[4,7]]=>0
[[1,2,3,4,6,7,9],[5,8]]=>2
[[1,2,4,5,8,9],[3,6,7]]=>7
[[1,2,4,5,6,7,9],[3,8]]=>0
[[1,2,4,5,7,9],[3,6,8]]=>5
[[1,2,3,5,6,8,9],[4],[7]]=>0
[[1,2,4,5,7,8,9],[3],[6]]=>7
[[1,2,3,5,7,8,9],[4],[6]]=>8
[[1,2,4,5,6,8,9],[3],[7]]=>8
[[1,3,4,6,7,9],[2,5,8]]=>3
[[1,2,4,5,6,8,9],[3,7]]=>8
[[1,2,3,5,6,7,9],[4],[8]]=>1
[[1,3,4,6,8,9],[2,5,7]]=>2
[[1,2,3,6,7,9],[4,5,8]]=>1
                    

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Description

The modular (standard) major index of a standard tableau.
The modular major index is the usual major index St000330The (standard) major index of a standard tableau. modulo $n$, where $n$ is the number of boxes in the standard tableau.

References

[1] Swanson, J. P. On the Existence of Tableaux with Given Modular Major Index arXiv:1701.04963

Code

def statistic(T):
    n = sum(T.shape())
    return T.standard_major_index() % n

Created

Feb 02, 2017 at 20:00 by Christian Stump

Updated

Feb 02, 2017 at 20:00 by Christian Stump