Combinatorial Counterpart of Some q-Series in the light of Colour Partitions

Abstract: The n-Colour partition, introduced by Agarwal and Andrews [1] are extended to (n + t)–color partitions where the parts of size n can come in (n + t), t ? 0, different colors. In the study of partition theory, the q-series plays an important role. The q-series are integral part of partition identities and hence for deep combinatorial study of analytic partition identities, it is important to know the combinatorial counterpart of q-series first. In this paper, the combinatorial counterpart of some analytic q-series has been given in the light of Colour Partitions