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Identifier
Values
[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