This paper provides insights into congruences and partition-theoretic interpretations involving q-series identities, suggesting deeper connections among partitions.
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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Biswas et al. (2025) studied this question.
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