New infinite families of congruences for 6-regular partitions

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2025年6月26日

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Nayandeep Deka Baruah,
Pranjal Talukdar

摘要

Let $b_6(n)$ $b_{6} (n)$ denote the number of 6-regular partitions of n. In this article, we prove some new infinite families of congruences modulo 3 and some individual congruences modulo 9 for $b_6(n)$ $b_{6} (n)$ using 5-dissections of some q-products, two of the well-known forty identities for the Rogers-Ramanujan functions of Ramanujan, Newman’s identities and a method of Radu. In the process, we also deduce some Kolberg-type congruences.