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Statistic identifier: St000206

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Collection: Integer partitions

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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 [[St000205]].

Each value in this statistic is greater than or equal to corresponding value in [[St000205]].


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

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Code:


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Statistic 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]             => 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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Created: May 19, 2014 at 11:29 by Per Alexandersson

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Last Updated: May 29, 2015 at 17:10 by Martin Rubey