October 2, 2025Open Access

Some New Congruences and Partition-Theoretic Interpretations for the Coefficients of Some Rogers-Ramanujan Type Identities

Key Points

The research reveals infinite families of congruences modulo powers of 2.
It provides partition-theoretic interpretations using overpartition and colour partition of positive integers.
The well-known Rogers-Ramanujan type identities are explored through q-series identity methods.
This analysis extends the understanding of partitions and congruences in the realm of combinatorial mathematics.

Abstract

Ramanujan listed several q-series identities in his lost notebook. The most well known q-series identities are the Rogers-Ramanujan type identities which are first discovered by Rogers and then rediscovered by Ramanujan. In this paper, we give partition-theoretic interpretations of some of the Rogers-Ramanujan type identities using overpartition and colour partition of positive integers, and prove infinite families of congruences modulo powers of 2.

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Cite This Study

Biswas et al. (Mon,) studied this question.

synapsesocial.com/papers/68de6f3a83cbc991d0a22998 https://doi.org/https://doi.org/10.48550/arxiv.2507.10020

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