A bijection for Euler's partition theorem in the spirit of Bressoud

TL;DR

This paper introduces a new bijection connecting odd and distinct partitions of integers, extending Bressoud's work and comparing it with classical and recent bijections to deepen understanding of Euler's partition theorem.

Contribution

It constructs a novel bijection between odd and distinct partitions that generalizes Bressoud's bijection and relates to classical and recent bijections.

Findings

New bijection extends Bressoud's work

Comparison with Glaisher, Sylvester, and Chen-Gao-Ji-Li bijections

Enhanced understanding of partition relationships

Abstract

For each positive integer $n$, we construct a bijection between the odd partitions and the distinct partitions of $n$ which extends Bressoud's bijection between the odd-and-distinct partitions of $n$ and the splitting partitions of $n$. We compare our bijection with the classical bijections of Glaisher and Sylvester, and also with a recent bijection due to Chen, Gao, Ji and Li.