- FindStat

Identifier

St001490: Skew partitions ⟶ ℤ

Values

=>
                            Cc0028;cc-rep
                            
                            
                            

                        [[1],[]]=>1
[[2],[]]=>1
[[1,1],[]]=>1
[[2,1],[1]]=>2
[[3],[]]=>1
[[2,1],[]]=>1
[[3,1],[1]]=>2
[[2,2],[1]]=>1
[[3,2],[2]]=>2
[[1,1,1],[]]=>1
[[2,2,1],[1,1]]=>2
[[2,1,1],[1]]=>2
[[3,2,1],[2,1]]=>3
[[4],[]]=>1
[[3,1],[]]=>1
[[4,1],[1]]=>2
[[2,2],[]]=>1
[[3,2],[1]]=>1
[[4,2],[2]]=>2
[[2,1,1],[]]=>1
[[3,2,1],[1,1]]=>2
[[3,1,1],[1]]=>2
[[4,2,1],[2,1]]=>3
[[3,3],[2]]=>1
[[4,3],[3]]=>2
[[2,2,1],[1]]=>1
[[3,3,1],[2,1]]=>2
[[3,2,1],[2]]=>2
[[4,3,1],[3,1]]=>3
[[2,2,2],[1,1]]=>1
[[3,3,2],[2,2]]=>2
[[3,2,2],[2,1]]=>2
[[4,3,2],[3,2]]=>3
[[1,1,1,1],[]]=>1
[[2,2,2,1],[1,1,1]]=>2
[[2,2,1,1],[1,1]]=>2
[[3,3,2,1],[2,2,1]]=>3
[[2,1,1,1],[1]]=>2
[[3,2,2,1],[2,1,1]]=>3
[[3,2,1,1],[2,1]]=>3
[[4,3,2,1],[3,2,1]]=>4
[[5],[]]=>1
[[4,1],[]]=>1
[[5,1],[1]]=>2
[[3,2],[]]=>1
[[4,2],[1]]=>1
[[5,2],[2]]=>2
[[3,1,1],[]]=>1
[[4,2,1],[1,1]]=>2
[[4,1,1],[1]]=>2
[[5,2,1],[2,1]]=>3
[[3,3],[1]]=>1
[[4,3],[2]]=>1
[[5,3],[3]]=>2
[[2,2,1],[]]=>1
[[3,3,1],[1,1]]=>2
[[3,2,1],[1]]=>1
[[4,3,1],[2,1]]=>2
[[4,2,1],[2]]=>2
[[5,3,1],[3,1]]=>3
[[3,2,2],[1,1]]=>1
[[4,3,2],[2,2]]=>2
[[4,2,2],[2,1]]=>2
[[5,3,2],[3,2]]=>3
[[2,1,1,1],[]]=>1
[[3,2,2,1],[1,1,1]]=>2
[[3,2,1,1],[1,1]]=>2
[[4,3,2,1],[2,2,1]]=>3
[[3,1,1,1],[1]]=>2
[[4,2,2,1],[2,1,1]]=>3
[[4,2,1,1],[2,1]]=>3
[[5,3,2,1],[3,2,1]]=>4
[[4,4],[3]]=>1
[[5,4],[4]]=>2
[[3,3,1],[2]]=>1
[[4,4,1],[3,1]]=>2
[[4,3,1],[3]]=>2
[[5,4,1],[4,1]]=>3
[[2,2,2],[1]]=>1
[[3,3,2],[2,1]]=>1
[[4,4,2],[3,2]]=>2
[[3,2,2],[2]]=>2
[[4,3,2],[3,1]]=>2
[[5,4,2],[4,2]]=>3
[[2,2,1,1],[1]]=>1
[[3,3,2,1],[2,1,1]]=>2
[[3,3,1,1],[2,1]]=>2
[[4,4,2,1],[3,2,1]]=>3
[[3,2,1,1],[2]]=>2
[[4,3,2,1],[3,1,1]]=>3
[[4,3,1,1],[3,1]]=>3
[[5,4,2,1],[4,2,1]]=>4
[[3,3,3],[2,2]]=>1
[[4,4,3],[3,3]]=>2
[[4,3,3],[3,2]]=>2
[[5,4,3],[4,3]]=>3
[[2,2,2,1],[1,1]]=>1
[[3,3,3,1],[2,2,1]]=>2
[[3,3,2,1],[2,2]]=>2
[[4,4,3,1],[3,3,1]]=>3
[[3,2,2,1],[2,1]]=>2
[[4,3,3,1],[3,2,1]]=>3
[[4,3,2,1],[3,2]]=>3
[[5,4,3,1],[4,3,1]]=>4
[[2,2,2,2],[1,1,1]]=>1
[[3,3,3,2],[2,2,2]]=>2
[[3,3,2,2],[2,2,1]]=>2
[[4,4,3,2],[3,3,2]]=>3
[[3,2,2,2],[2,1,1]]=>2
[[4,3,3,2],[3,2,2]]=>3
[[4,3,2,2],[3,2,1]]=>3
[[5,4,3,2],[4,3,2]]=>4
[[1,1,1,1,1],[]]=>1
[[2,2,2,2,1],[1,1,1,1]]=>2
[[2,2,2,1,1],[1,1,1]]=>2
[[3,3,3,2,1],[2,2,2,1]]=>3
[[2,2,1,1,1],[1,1]]=>2
[[3,3,2,2,1],[2,2,1,1]]=>3
[[3,3,2,1,1],[2,2,1]]=>3
[[4,4,3,2,1],[3,3,2,1]]=>4
[[2,1,1,1,1],[1]]=>2
[[3,2,2,2,1],[2,1,1,1]]=>3
[[3,2,2,1,1],[2,1,1]]=>3
[[4,3,3,2,1],[3,2,2,1]]=>4
[[3,2,1,1,1],[2,1]]=>3
[[4,3,2,2,1],[3,2,1,1]]=>4
[[4,3,2,1,1],[3,2,1]]=>4
[[5,4,3,2,1],[4,3,2,1]]=>5
                    

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Description

The number of connected components of a skew partition.

Code

def statistic(la):
    return len(la.cell_poset().connected_components())

Created

Oct 30, 2019 at 12:59 by Martin Rubey

Updated

Oct 30, 2019 at 12:59 by Martin Rubey