T Kathiravan ; Dipramit Majumdar ; Usha Sangale - Infinite families of congruences modulo $2$ for $(\ell, k)$-regular partitions

hrj:13034 - Hardy-Ramanujan Journal, February 15, 2024, Volume 46 - 2023 - https://doi.org/10.46298/hrj.2024.13034
Infinite families of congruences modulo $2$ for $(\ell, k)$-regular partitionsArticle

Authors: T Kathiravan 1; Usha Sangale 2; Dipramit Majumdar 1

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.


Volume: Volume 46 - 2023
Published on: February 15, 2024
Accepted on: February 15, 2024
Submitted on: February 9, 2024
Keywords: Partition function,Regular-partition,Ramanujan congruences,11P83, 05A17,[MATH]Mathematics [math]

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