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.

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, 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

Offset

0,3

Comments

Row sums give A000041.

Links

Table of n, a(n) for n=0..85.

FindStat - Combinatorial Statistic Finder, Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight.

J. De Loera and T. B. McAllister, Vertices of Gelfand-Tsetlin polytopes, arXiv:math/0309329 [math.CO], 2003, MathSciNet:2096742.

Example

Triangle begins:
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,
8,1,0,0,0,0,0,0,2,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,2,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
...

Crossrefs

Cf. A000041, A264035, A264048, A264049.

Sequence in context: A118141 A343767 A175210 * A264035 A082876 A096099

Adjacent sequences: A264044 A264045 A264046 * A264048 A264049 A264050

Keyword

nonn,tabf

Author

Christian Stump, Nov 01 2015

Status

approved