On Multiplicity of Parts in n-Colour Compositions

Abstract

The first chapter introduces the concepts of partitions, compositions and n-colour composi- tions. It also includes standard results on compositions and n-colour compositions. Thus, this chapter provides the required toolkit to solve higher level problems. The second chapter mainly focus on multiplicity of parts in random composition of an integer. Here we construct two variable generating function for a particular part size in composition and discuss mean and variance of the multiplicity of part size in composition. In third chapter we extend the results of chapter 2 for n-colour compositions. Here we discuss expected value of multiplicity of a part size in randomly choosen n-colour composition.