Study of Gollnitz-Gordon Identities

Abstract

In this thesis, we studied Combinatorial interpretation of generalized q - series given by Agarwal in 1986 (A.K. Agarwal, On a Generalized Partition Theorem, J. Indian Math. Soc. Vol. 50 (1986), pp. 185-190) using ordinary partitions. Recently Agarwal and Rana in 2009 (A.K. Agarwal and M. Rana, New Combinatorial Version of G¨llnitz - Gordon identities, Utilitas Mathematica., Vol. 79(2009), pp.o 145-156 ) extended the interpretation given by agarwal in 1986 using n - colour partitions which leads to an infinite family of 2 - way combinatorial identities. In some particular cases these 2 - way combinatorial identities are extended to a 3 - way combinatorial identities which gives combinatorial interpretations of G¨llnitz-o Gordon identities using ordinary partition discussed in Chapter 2 and using n - colour partition discussed in Chapter 3. Chapter 1 is devoted to elementary study of partition Theory.