ON THE ORDINARY AND SIGNED G¨ OLLNITZ-GORDON PARTITIONS

Print ISSN: 0972-7752

Abstract

In [Bull. Amer. Math. Soc. 44 (2007) 561—573], George Andrews introduced the concept of a “signed partition,” i.e. a representation of a positive integer as an unordered sum of integers, some possibly negative. In that paper, Andrews provides an alternate combinatorial interpretation, in terms of signed partitions, of a certain q-series identity associated with the G¨ollnitz-Gordon partition theorem. In this paper, I present a bijection between the “ordinary” and “signed” G¨ollnitz-Gordon partitions.

Keywords and Phrases

Integer partitions, G¨ollnitz-Gordon identity.

A.M.S. subject classification

05A17.

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