- FindStat

Identifier

St000205: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

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

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Description

Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight.
Given $\lambda$ count how many integer partitions $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.

References

[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742

Created

May 19, 2014 at 11:16 by Per Alexandersson

Updated

May 29, 2015 at 17:10 by Martin Rubey