A264048 Triangle read by rows: T(n,k) (n>=1, k>=1) 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 integral.

1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1

Offset: 1

Author

Christian Stump, Nov 02 2015

Keywords

• nonn
• tabf

Comments

Row sums give A000041, n >= 1.

Examples

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

Links

• FindStat - Combinatorial Statistic Finder, Number of 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.

Crossrefs

Cf. A000041, A264035, A264047, A264049.