Authors: Nayandeep Deka Baruah ¹; Hirakjyoti Das ¹

• 1 Tezpur University

Let $b_{\ell;3}(n)$ denote the number of $\ell$-regular partitions of $n$ in 3 colours. In this paper, we find some general generating functions and new infinite families of congruences modulo arbitrary powers of $3$ when $\ell\in\{9,27\}$. For instance, for positive integers $n$ and $k$, we have

• 05A15 - Exact enumeration problems, generating functions
• 05A17 - Combinatorial aspects of partitions of integers
• 11P83 - Partitions; congruences and congruential restrictions