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Identifier
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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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.
References
[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742
Created
May 19, 2014 at 11:32 by Per Alexandersson
Updated
May 29, 2015 at 17:10 by Martin Rubey