- FindStat

Identifier

St001488: Skew partitions ⟶ ℤ

Values

=>
                            Cc0028;cc-rep
                            
                            
                            

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

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Description

The number of corners of a skew partition.
This is also known as the number of removable cells of the skew partition.

Code

def statistic(L):
    return len(set(L.inner_corners()).union(L.outer_corners()))

Created

Oct 28, 2019 at 19:23 by Martin Rubey

Updated

Nov 06, 2019 at 16:39 by Martin Rubey