On lattice paths and q-series

Abstract

In this thesis, we study one combinatorial tool, particularly, lattice paths. In subsequent chapters we interpret lattice paths as the generating functions for certain q-series. The lattice paths are considered as a standard combinatorial tool which were introduced by Agarwal and Bressoud (Lattice paths and multiple basic hypergeometric series, Pacific J. Math. 136(2) (1989), 209-228) to understand the enumeration of q-series and gave a new insights in the field of combinatorics. In Chapter 1 we give some basic definitions, notations and preliminary results. In Chapter 2 we study lattice paths as the generating functions for many q-series. In Chapter 3 we provide some generalized q-series and study the combinatorial interpretations of the given q-series using the lattice paths.