منابع مشابه
The Point Partition Numbers of Closed 2-manifolds
Let M be a closed 2-manifold. The chromatic number of M is defined to be the maximum chromatic number of all graphs which can be imbedded in M. The famous Four Colour Conjecture states that the chromatic number of the sphere is four. One of the oddities of mathematics is that the chromatic number of the familiar sphere is still unknown, although the chromatic number of every other closed 2-mani...
متن کاملRamsey-type numbers involving graphs and hypergraphs with large girth
For a set of integers S, define ( S APk ) to be the k-uniform hypergraph with vertex set S and hyperedges corresponding to the set of all arithmetic progression of length k in S. Similarly, for a graph H, define ( H Kk ) to be the ( k 2 ) -uniform hypergraph on the vertex set E(H) with hyperedges corresponding to the edge sets of all copies of Kk in H. Also, we say that a k-uniform hypergraph h...
متن کاملPartition Parameters for Girth Maximum (m, r) BTUs
This paper describes the calculation of the optimal partition parameters such that the girth maximum (m, r) Balanced Tanner Unit lies in family of BTUs specified by them using a series of proved results and thus creates a framework for specifying a search problem for finding the girth maximum (m, r) BTU. Several open questions for girth maximum (m, r) BTU have been raised.
متن کاملSet partition statistics and q-Fibonacci numbers
We consider the set partition statistics ls and rb introduced by Wachs and White and investigate their distribution over set partitions avoiding certain patterns. In particular, we consider those set partitions avoiding the pattern 13/2, Πn(13/2), and those avoiding both 13/2 and 123, Πn(13/2, 123). We show that the distribution over Πn(13/2) enumerates certain integer partitions, and the distr...
متن کاملm-Partition Boards and Poly-Stirling Numbers
We define a generalization of the Stirling numbers of the first and second kinds and develop a new rook theory model to give combinatorial interpretations to these numbers. These rook-theoretic interpretations are used to give a direct combinatorial proof that two associated matrices are inverses of each other. We also give combinatorial interpretations of the numbers in terms of certain collec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0371734-8