Andrews-Gordon Type Series for Schur's Partition Identity

Kağan Kurşungöz

Published 2018-12-25Version 1

We construct an evidently positive multiple series as a generating function for partitions satisfying the multiplicity condition in Schur's partition theorem. Refinements of the series when parts in the said partitions are classified according to their parities or values mod 3 are also considered. Direct combinatorial interpretations of the series are provided.