On partitions of bipartite numbers

Abstract

In this thesis, we are concerned with the multiplicative partitions. he main purpose of the thesis is to find a recursive formula for the ultipartite partition function and to estimate the number of mutipli- ative partitions of bipartite numbers. n Chapter 1, we consider the multiplicative partitions of bipartite umbers. Canfield, Erd\"os, Pomerance, Hughes, Shallit, Mattics, odd and others have estimated the number of multiplicative partitions f non-bipartite numbers. Landman and Raymond has recently extended the dea of multiplicative partitions to bipartite numbers. In this chapter e estimate the number of multiplicative partitions of bipartite numbers. n Chapter 2, we consider the multipartite partition functions. Up to ow there is no known simple infinite series that is useful in treating he multiplicative partition functions. In this chapter we derive ecursive fomulas for the multipartite partition functions. n Chapter 3, applying the theory of partitions of bipartite numbers to oding theory, we find good upper bounds for the maximum number of ne-error-correcting codes among possible codes.