On n- color Partitions and Combinatorics.

Abstract

The present dissertation contains a detail study of investigations carried out by various authors on enumerative combinatorics using n-color partitions of certain q-series. The whole work is divided into three chapters. Chapter 1 is introductory including elementary definitions, notations and generating functions which will be required for later chapters. This chapter includes some celebrated identities such as Rogers-Ramanujan Identities and Gollnitz-Gordan Identities. In Chapter 2, we have discussed n-color partitions introduced by Agarwal and Andrews ["N copies of N", J. Combin. Theory Ser. A 45, (1987), 40-49]. This chapter is further devoted to the study of (n + t)-color partitions. In Chapter 3, we have done the survey of further advances in n-color partitions. It particularly include the combinatorial interpretations of q-series using n-color partitions, further Rogers-Ramanujan type Identities for n-color partitions are also explored.