Combinatorial identities related to vector partitions

Research Report MRR96-063

Combinatorial identities related to vector partitions

Geoffrey B. Campbell

Abstract: In this paper we present a combinatorial identity which is a 2-D vector partition analogue of the q-binomial theorem. Its corollaries are analogous to classical results by Euler, Cauchy and Gauss. Also implied is a generalization to n variables which may be an opening to new work on vector partitions. Later we give functional equations for generalized Vector or Multipartite partition generating functions as given in Andrews' account of the theory of partitions. (see Andrews [1, chapter 12])

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