- FindStat

edit this statistic or download as text // json

Identifier

St001803: Standard tableaux ⟶ ℤ

Values

=>
                            Cc0007;cc-rep
                            
                            
                            

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

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Description

The maximal overlap of the cylindrical tableau associated with a tableau.
A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
In particular, the statistic equals $0$, if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.

Code

def statistic(T):
    if not T:
        return 0
    w = len(T[0])
    l = len(T)
    d = 0
    while d < l and len(T[d]) == w and T[0][w-1] < T[l-1-d][0]:
        d += 1
    return d

Created

Jun 06, 2022 at 19:26 by Martin Rubey

Updated

Jun 06, 2022 at 19:26 by Martin Rubey