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Statistic identifier: St000208

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Collection: Integer partitions

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Description: Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight.

Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that
$P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has only integer lattice points as vertices.

See also [[St000205]], [[St000206]] and [[St000207]].

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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]               => 1
[2]               => 2
[1,1]             => 1
[3]               => 3
[2,1]             => 2
[1,1,1]           => 1
[4]               => 5
[3,1]             => 4
[2,2]             => 3
[2,1,1]           => 2
[1,1,1,1]         => 1
[5]               => 7
[4,1]             => 6
[3,2]             => 4
[3,1,1]           => 4
[2,2,1]           => 2
[2,1,1,1]         => 2
[1,1,1,1,1]       => 1
[6]               => 11
[5,1]             => 10
[4,2]             => 8
[4,1,1]           => 7
[3,3]             => 6
[3,2,1]           => 4
[3,1,1,1]         => 4
[2,2,2]           => 3
[2,2,1,1]         => 2
[2,1,1,1,1]       => 2
[1,1,1,1,1,1]     => 1
[7]               => 15
[6,1]             => 14
[5,2]             => 12
[5,1,1]           => 11
[4,3]             => 8
[4,2,1]           => 6
[4,1,1,1]         => 7
[3,3,1]           => 5
[3,2,2]           => 5
[3,2,1,1]         => 4
[3,1,1,1,1]       => 4
[2,2,2,1]         => 2
[2,2,1,1,1]       => 2
[2,1,1,1,1,1]     => 2
[1,1,1,1,1,1,1]   => 1
[8]               => 22
[7,1]             => 21
[6,2]             => 19
[6,1,1]           => 17
[5,3]             => 15
[5,2,1]           => 9
[5,1,1,1]         => 12
[4,4]             => 12
[4,3,1]           => 9
[4,2,2]           => 9
[4,2,1,1]         => 7
[4,1,1,1,1]       => 7
[3,3,2]           => 5
[3,3,1,1]         => 5
[3,2,2,1]         => 3
[3,2,1,1,1]       => 4
[3,1,1,1,1,1]     => 4
[2,2,2,2]         => 3
[2,2,2,1,1]       => 2
[2,2,1,1,1,1]     => 2
[2,1,1,1,1,1,1]   => 2
[1,1,1,1,1,1,1,1] => 1

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Created: May 19, 2014 at 11:36 by Per Alexandersson

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