• 1 Indian Institute of Technology Madras [IIT Madras]
• 2 Swami Ramanand Teerth Marathwada University, Nanded

Let $b_{\ell, k}(n)$ denote the number of $(\ell, k)$-regular partition of $n$. Recently, some congruences modulo $2$ for $(3, 8), (4, 7)$-regular partition and modulo $8$, modulo $9$ and modulo $12$ for $(4, 9)$-regular partition has been studied. In this paper, we use theta function identities and Newman results to prove some infinite families of congruences modulo $2$ for $(2, 7)$, $(5, 8)$, $(4, 11)$-regular partition and modulo $4$ for $(4, 5)$-regular partition.

• 05A17 - Combinatorial aspects of partitions of integers
• 11P83 - Partitions; congruences and congruential restrictions