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

1,57

Comments

Row sums give A000041, n >= 1.

Links

Table of n, a(n) for n=1..101.

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.

Example

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,
...

Crossrefs

Cf. A000041, A264035, A264047, A264049.

Sequence in context: A353337 A351907 A357374 * A101257 A321892 A225542

Adjacent sequences: A264045 A264046 A264047 * A264049 A264050 A264051

Keyword

nonn,tabf

Author

Christian Stump, Nov 02 2015

Status

approved