Legendre theorems for a class of partitions with initial repetitions

TL;DR

This paper explores a specific subclass of partitions with initial repetitions, establishing Legendre theorems and linking them to Rogers-Ramanujan identities, thus providing new partition theoretic interpretations.

Contribution

It introduces new Legendre theorems for a subclass of initial repetition partitions and connects these to classical Rogers-Ramanujan identities.

Findings

Legendre theorems established for the subclass

Partition interpretations of Rogers-Ramanujan identities

Enhanced understanding of initial repetition partitions

Abstract

Partitions with initial repetitions were introduced by George Andrews. We consider a subclass of these partitions and find Legendre theorems associated with their respective partition functions. The results in turn provide partition theoretic interpretations of some Rogers-Ramanujan identities due to Lucy J. Slater.