Glaisher combinatorics of regular partitions

TL;DR

This paper introduces a new class of regular partitions called $(r_{1},...,r_{m})$-class regular partitions, extending existing concepts, and presents a partition identity using Glaisher correspondence.

Contribution

It defines a generalized notion of regular partitions and establishes a new partition identity via Glaisher correspondence.

Findings

Introduction of $(r_{1},...,r_{m})$-class regular partitions

Derivation of a partition identity using Glaisher correspondence

Extension of classical regular partition concepts

Abstract

Extending the notion of $r$-(class) regular partitions, we define $(r_{1},...,r_{m})$-class regular partitions. A partition identity is presented and described by making use of the Glaisher correspondence.