منابع مشابه
Restricted partitions
We prove a known partitions theorem by Bell in an elementary and constructive way. Our proof yields a simple recursive method to compute the corresponding Sylvester polynomials for the partition. The previous known methods to obtain these polynomials are in general not elementary. 1. Proof of Bell's theorem. The main purpose of this section is to prove the following theorem, originally proved b...
متن کاملRestricted Partitions Elementary Methods
In [1] certain restricted partitions were studied in an elementary way. In this article we study other problem about restricted partitions. We prove the following theorem in a direct way and using elementary methods ( combinatory and mathematical induction). Theorem 1. Let n be a positive integer, and let A1, A2, . . . , An be n positive integers. Then, for all positive integers N = MK + r, the...
متن کاملEfficient Computation of Restricted Partitions
Have you ever wondered how many ways the total of 5 dollars can be made with coins having cent values {1, 2, 5, 10, 20, 50, 100, 200}? Would you like to take a guess at how many ways there are? Would you be surprised if I told you there were 6295434? Maybe we should tone it down a bit and ask how many ways there are to make 50 cents. There are still 451! Lets step back once more and determine h...
متن کاملConvex p-partitions of bipartite graphs
A set of vertices X of a graph G is convex if it contains all vertices on shortest paths between vertices of X. We prove that for fixed p ≥ 1, all partitions of the vertex set of a bipartite graph into p convex sets can be found in polynomial time.
متن کاملRestricted 2 { factors in Bipartite
The k{restricted 2{factor problem is that of nding a spanning subgraph consisting of disjoint cycles with no cycle of length less than or equal to k. It is a generalization of the well known Hamilton cycle problem and is equivalent to this problem when n 2 k n ? 1. This paper considers necessary and suucient conditions, algorithms, and polyhedral conditions for 2{factors in bipartite graphs and...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.19.221