cp's OEIS Frontend

A264047 Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of integer partitions lambda of n such that there are k compositions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral.

%I A264047 #9 Nov 25 2015 21:34:39
%S A264047 1,1,2,3,5,5,2,6,3,0,1,0,0,1,7,1,0,0,0,0,0,2,2,0,0,1,0,0,0,0,1,1,8,1,
%T A264047 0,0,0,0,0,0,2,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,2,0,0,0,0,
%U A264047 0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1
%N A264047 Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of integer partitions lambda of n such that there are k compositions mu such that the Gelfand-Tsetlin polytope for lambda and mu is non-integral.
%C A264047 Row sums give A000041.
%H A264047 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000206">Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight</a>.
%H A264047 J. De Loera and T. B. McAllister, <a href="http://arxiv.org/abs/math/0309329">Vertices of Gelfand-Tsetlin polytopes</a>, arXiv:math/0309329 [math.CO], 2003, MathSciNet:2096742.
%e A264047 Triangle begins:
%e A264047 1,
%e A264047 1,
%e A264047 2,
%e A264047 3,
%e A264047 5,
%e A264047 5,2,
%e A264047 6,3,0,1,0,0,1,
%e A264047 7,1,0,0,0,0,0,2,2,0,0,1,0,0,0,0,1,1,
%e A264047 8,1,0,0,0,0,0,0,2,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,2,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
%e A264047 ...
%Y A264047 Cf. A000041, A264035, A264048, A264049.
%K A264047 nonn,tabf
%O A264047 0,3
%A A264047 _Christian Stump_, Nov 01 2015