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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]=>3 [4,1,1]=>0 [3,3]=>1 [3,2,1]=>6 [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]=>7 [5,1,1]=>0 [4,3]=>11 [4,2,1]=>16 [4,1,1,1]=>0 [3,3,1]=>17 [3,2,2]=>8 [3,2,1,1]=>8 [3,1,1,1,1]=>0 [2,2,2,1]=>7 [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]=>15 [6,1,1]=>0 [5,3]=>31 [5,2,1]=>43 [5,1,1,1]=>0 [4,4]=>14 [4,3,1]=>53 [4,2,2]=>28 [4,2,1,1]=>31 [4,1,1,1,1]=>0 [3,3,2]=>39 [3,3,1,1]=>24 [3,2,2,1]=>30 [3,2,1,1,1]=>11 [3,1,1,1,1,1]=>0 [2,2,2,2]=>8 [2,2,2,1,1]=>8 [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 integer composition weight.
Given $\lambda$ count how many integer compositions $w$ (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.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
References
[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742
Created
May 19, 2014 at 11:29 by Per Alexandersson
Updated
May 29, 2015 at 17:10 by Martin Rubey