Study of Gaussian Polynomial

Abstract

In the application of Partition theory, such as in statistics mechanics, computer science, special functions, algebra, theoretical physics, combinatorics, we are often interested in restricted partitions, that is, partition in which several restrictions are imposed. For example, partition in which the largest part is say, N and the number of parts is M.So here in this thesis we study restricted partition as generating function of some q-series. Chapter 1 deals with elementary de nitions and results. In Chapter 2, we study Gaussian Polynomial, the polynomial G(N;M; q) = (q; q)N+M (q; q)N(q; q)M which were rst studied by Gauss in 1863. Lastly, in Chapter 3, we interpret some q-series as generating function of some restricted partition function.