Identifier
Identifier
Values
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 0
[3] generating graphics... => 0
[2,1] generating graphics... => 0
[1,1,1] generating graphics... => 0
[4] generating graphics... => 0
[3,1] generating graphics... => 0
[2,2] generating graphics... => 0
[2,1,1] generating graphics... => 0
[1,1,1,1] generating graphics... => 0
[5] generating graphics... => 0
[4,1] generating graphics... => 0
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 0
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 0
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 0
[5,1] generating graphics... => 0
[4,2] generating graphics... => 3
[4,1,1] generating graphics... => 0
[3,3] generating graphics... => 1
[3,2,1] generating graphics... => 6
[3,1,1,1] generating graphics... => 0
[2,2,2] generating graphics... => 1
[2,2,1,1] generating graphics... => 1
[2,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1] generating graphics... => 0
[7] generating graphics... => 0
[6,1] generating graphics... => 0
[5,2] generating graphics... => 7
[5,1,1] generating graphics... => 0
[4,3] generating graphics... => 11
[4,2,1] generating graphics... => 16
[4,1,1,1] generating graphics... => 0
[3,3,1] generating graphics... => 17
[3,2,2] generating graphics... => 8
[3,2,1,1] generating graphics... => 8
[3,1,1,1,1] generating graphics... => 0
[2,2,2,1] generating graphics... => 7
[2,2,1,1,1] generating graphics... => 1
[2,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1] generating graphics... => 0
[8] generating graphics... => 0
[7,1] generating graphics... => 0
[6,2] generating graphics... => 15
[6,1,1] generating graphics... => 0
[5,3] generating graphics... => 31
[5,2,1] generating graphics... => 43
[5,1,1,1] generating graphics... => 0
[4,4] generating graphics... => 14
[4,3,1] generating graphics... => 53
[4,2,2] generating graphics... => 28
[4,2,1,1] generating graphics... => 31
[4,1,1,1,1] generating graphics... => 0
[3,3,2] generating graphics... => 39
[3,3,1,1] generating graphics... => 24
[3,2,2,1] generating graphics... => 30
[3,2,1,1,1] generating graphics... => 11
[3,1,1,1,1,1] generating graphics... => 0
[2,2,2,2] generating graphics... => 8
[2,2,2,1,1] generating graphics... => 8
[2,2,1,1,1,1] generating graphics... => 1
[2,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1] generating graphics... => 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