Analytic proof of the partition identity $A_{5,3,3}(n)=B_{5,3,3}^0(n)$

Abstract

In this paper we give an analytic proof of the identity $A_{5,3,3}(n)=B_{5,3,3}^0(n)$, where $A_{5,3,3}(n)$ counts the number of partitions of $n$ subject to certain restrictions on their parts, and $B_{5,3,3}^0(n)$ counts the number of partitions of $n$ subject to certain other restrictions on their parts, both too long to be stated in the abstract. Our proof establishes actually a refinement of that partition identity. The original identity was first discovered by the first author jointly with M. Ruby Salestina and S. R. Sudarshan in ["A new theorem on partitions," Proc. Int. Conference on Special Functions, IMSC, Chennai, India, September 23-27, 2002; to appear], where it was also given a combinatorial proof, thus responding a question of Andrews.

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