# A partition bijection related to the Rogers--Selberg identities and Gordon's theorem

## TL;DR

This paper constructs a bijective correspondence between partitions related to Rogers-Selberg identities and Gordon's theorem, revealing new combinatorial insights and connections in partition theory.

## Contribution

It introduces a novel bijection linking Rogers-Selberg identities with Gordon's theorem, expanding understanding of partition identities and their combinatorial structures.

## Key findings

- Established a bijection between specific partition sets
- Connected Rogers-Selberg identities with Gordon's theorem
- Explored implications for Bressoud's even modulus analog

## Abstract

We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.