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Statistic identifier: St000207

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Collection: Integer partitions

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Description: Number of 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 integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has all vertices in integer lattice points.




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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]               => 4
[2,1]             => 3
[1,1,1]           => 1
[4]               => 8
[3,1]             => 7
[2,2]             => 5
[2,1,1]           => 4
[1,1,1,1]         => 1
[5]               => 16
[4,1]             => 15
[3,2]             => 12
[3,1,1]           => 11
[2,2,1]           => 7
[2,1,1,1]         => 5
[1,1,1,1,1]       => 1
[6]               => 32
[5,1]             => 31
[4,2]             => 26
[4,1,1]           => 26
[3,3]             => 23
[3,2,1]           => 17
[3,1,1,1]         => 16
[2,2,2]           => 12
[2,2,1,1]         => 11
[2,1,1,1,1]       => 6
[1,1,1,1,1,1]     => 1
[7]               => 64
[6,1]             => 63
[5,2]             => 54
[5,1,1]           => 57
[4,3]             => 45
[4,2,1]           => 38
[4,1,1,1]         => 42
[3,3,1]           => 27
[3,2,2]           => 33
[3,2,1,1]         => 30
[3,1,1,1,1]       => 22
[2,2,2,1]         => 14
[2,2,1,1,1]       => 16
[2,1,1,1,1,1]     => 7
[1,1,1,1,1,1,1]   => 1
[8]               => 128
[7,1]             => 127
[6,2]             => 110
[6,1,1]           => 120
[5,3]             => 89
[5,2,1]           => 74
[5,1,1,1]         => 99
[4,4]             => 94
[4,3,1]           => 54
[4,2,2]           => 73
[4,2,1,1]         => 64
[4,1,1,1,1]       => 64
[3,3,2]           => 42
[3,3,1,1]         => 54
[3,2,2,1]         => 42
[3,2,1,1,1]       => 48
[3,1,1,1,1,1]     => 29
[2,2,2,2]         => 26
[2,2,2,1,1]       => 25
[2,2,1,1,1,1]     => 22
[2,1,1,1,1,1,1]   => 8
[1,1,1,1,1,1,1,1] => 1

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Created: May 19, 2014 at 11:32 by Per Alexandersson

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