edit this statistic or download as text // json
Identifier
Values
=>
Cc0002;cc-rep
[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