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Identifier
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