- FindStat

Identifier

St000075: Standard tableaux ⟶ ℤ

Values

=>
                            Cc0007;cc-rep
                            
                            
                            

                        [[1]]=>1
[[1,2]]=>1
[[1],[2]]=>1
[[1,2,3]]=>1
[[1,3],[2]]=>2
[[1,2],[3]]=>2
[[1],[2],[3]]=>1
[[1,2,3,4]]=>1
[[1,3,4],[2]]=>3
[[1,2,4],[3]]=>3
[[1,2,3],[4]]=>3
[[1,3],[2,4]]=>2
[[1,2],[3,4]]=>2
[[1,4],[2],[3]]=>3
[[1,3],[2],[4]]=>3
[[1,2],[3],[4]]=>3
[[1],[2],[3],[4]]=>1
[[1,2,3,4,5]]=>1
[[1,3,4,5],[2]]=>4
[[1,2,4,5],[3]]=>4
[[1,2,3,5],[4]]=>4
[[1,2,3,4],[5]]=>4
[[1,3,5],[2,4]]=>2
[[1,2,5],[3,4]]=>3
[[1,3,4],[2,5]]=>3
[[1,2,4],[3,5]]=>2
[[1,2,3],[4,5]]=>3
[[1,4,5],[2],[3]]=>4
[[1,3,5],[2],[4]]=>2
[[1,2,5],[3],[4]]=>4
[[1,3,4],[2],[5]]=>4
[[1,2,4],[3],[5]]=>2
[[1,2,3],[4],[5]]=>4
[[1,4],[2,5],[3]]=>3
[[1,3],[2,5],[4]]=>2
[[1,2],[3,5],[4]]=>3
[[1,3],[2,4],[5]]=>3
[[1,2],[3,4],[5]]=>2
[[1,5],[2],[3],[4]]=>4
[[1,4],[2],[3],[5]]=>4
[[1,3],[2],[4],[5]]=>4
[[1,2],[3],[4],[5]]=>4
[[1],[2],[3],[4],[5]]=>1
[[1,2,3,4,5,6]]=>1
[[1,3,4,5,6],[2]]=>5
[[1,2,4,5,6],[3]]=>5
[[1,2,3,5,6],[4]]=>5
[[1,2,3,4,6],[5]]=>5
[[1,2,3,4,5],[6]]=>5
[[1,3,5,6],[2,4]]=>5
[[1,2,5,6],[3,4]]=>4
[[1,3,4,6],[2,5]]=>5
[[1,2,4,6],[3,5]]=>5
[[1,2,3,6],[4,5]]=>4
[[1,3,4,5],[2,6]]=>4
[[1,2,4,5],[3,6]]=>5
[[1,2,3,5],[4,6]]=>5
[[1,2,3,4],[5,6]]=>4
[[1,4,5,6],[2],[3]]=>5
[[1,3,5,6],[2],[4]]=>5
[[1,2,5,6],[3],[4]]=>5
[[1,3,4,6],[2],[5]]=>5
[[1,2,4,6],[3],[5]]=>5
[[1,2,3,6],[4],[5]]=>5
[[1,3,4,5],[2],[6]]=>5
[[1,2,4,5],[3],[6]]=>5
[[1,2,3,5],[4],[6]]=>5
[[1,2,3,4],[5],[6]]=>5
[[1,3,5],[2,4,6]]=>2
[[1,2,5],[3,4,6]]=>3
[[1,3,4],[2,5,6]]=>3
[[1,2,4],[3,5,6]]=>2
[[1,2,3],[4,5,6]]=>3
[[1,4,6],[2,5],[3]]=>12
[[1,3,6],[2,5],[4]]=>12
[[1,2,6],[3,5],[4]]=>4
[[1,3,6],[2,4],[5]]=>12
[[1,2,6],[3,4],[5]]=>12
[[1,4,5],[2,6],[3]]=>4
[[1,3,5],[2,6],[4]]=>12
[[1,2,5],[3,6],[4]]=>12
[[1,3,4],[2,6],[5]]=>12
[[1,2,4],[3,6],[5]]=>12
[[1,2,3],[4,6],[5]]=>4
[[1,3,5],[2,4],[6]]=>12
[[1,2,5],[3,4],[6]]=>12
[[1,3,4],[2,5],[6]]=>4
[[1,2,4],[3,5],[6]]=>12
[[1,2,3],[4,5],[6]]=>12
[[1,5,6],[2],[3],[4]]=>5
[[1,4,6],[2],[3],[5]]=>5
[[1,3,6],[2],[4],[5]]=>5
[[1,2,6],[3],[4],[5]]=>5
[[1,4,5],[2],[3],[6]]=>5
[[1,3,5],[2],[4],[6]]=>5
[[1,2,5],[3],[4],[6]]=>5
[[1,3,4],[2],[5],[6]]=>5
[[1,2,4],[3],[5],[6]]=>5
[[1,2,3],[4],[5],[6]]=>5
[[1,4],[2,5],[3,6]]=>3
[[1,3],[2,5],[4,6]]=>2
[[1,2],[3,5],[4,6]]=>3
[[1,3],[2,4],[5,6]]=>3
[[1,2],[3,4],[5,6]]=>2
[[1,5],[2,6],[3],[4]]=>4
[[1,4],[2,6],[3],[5]]=>5
[[1,3],[2,6],[4],[5]]=>5
[[1,2],[3,6],[4],[5]]=>4
[[1,4],[2,5],[3],[6]]=>4
[[1,3],[2,5],[4],[6]]=>5
[[1,2],[3,5],[4],[6]]=>5
[[1,3],[2,4],[5],[6]]=>4
[[1,2],[3,4],[5],[6]]=>5
[[1,6],[2],[3],[4],[5]]=>5
[[1,5],[2],[3],[4],[6]]=>5
[[1,4],[2],[3],[5],[6]]=>5
[[1,3],[2],[4],[5],[6]]=>5
[[1,2],[3],[4],[5],[6]]=>5
[[1],[2],[3],[4],[5],[6]]=>1
[[1,2,3,4,5,6,7]]=>1
                    

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Description

The orbit size of a standard tableau under promotion.

References

[1] Schützenberger, M. P. Promotion des morphismes d'ensembles ordonnés MathSciNet:0299539
[2] Stanley, R. P. Promotion and evacuation MathSciNet:2515772

Code

def statistic(self):
    n = self.size() -1
    new = self.promotion(n)
    i = 1
    while new != self:
        new = new.promotion(n)
        i = i+1
    else:
        return i

Created

Jun 11, 2013 at 15:46 by Jessica Striker

Updated

Oct 16, 2015 at 11:54 by Christian Stump