edit this statistic or download as text // json
Identifier
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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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 St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight., St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. and St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight..
References
[1] De Loera, Jesús A., McAllister, T. B. Vertices of Gelfand-Tsetlin polytopes MathSciNet:2096742
Created
May 19, 2014 at 11:36 by Per Alexandersson
Updated
May 29, 2015 at 17:10 by Martin Rubey