# Andrews-Gordon Type Series for Schur's Partition Identity

## TL;DR

This paper develops a positive multiple series as a generating function for partitions related to Schur's theorem, with refinements based on parity and modular classifications, and provides combinatorial interpretations.

## Contribution

It introduces a new positive series representation for Schur's partition identities, including refinements and combinatorial interpretations.

## Key findings

- Constructed a positive multiple series generating function.
- Provided refinements based on parity and mod 3 classifications.
- Offered direct combinatorial interpretations.

## Abstract

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.