# Some congruences for $(\\ell, k)$ and $(\\ell, k, r)$-regular partitions

Source: [Some congruences for $(\\ell, k)$ and $(\\ell, k, r)$-regular partitions](<https://www.sota2.com/research/paper/68fa5a3d1e209131ce9be130>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T16:22:39.889Z

Authors: T Kathiravan, K Srinivas, Usha K Sangale

Published: 2023-03-24T10:40:52.000Z

## Abstract

Let $b\_{\\ell, k}(n), b\_{\\ell, k, r}(n)$ count the number of $(\\ell, k)$, $(\\ell, k, r)$-regular partitions respectively. In this paper we shall derive infinite families of congruences for $b\_{\\ell, k}(n)$ modulo $2$ when $ (\\ell, k) = (3,8), (4, 7)$, for $b\_{\\ell, k}(n)$ modulo $8$, modulo $9$ and modulo $12$ when $(\\ell, k) = (4, 9)$ and $b\_{\\ell, k, r}(n)$ modulo $2$ when $(\\ell, k, r) = (3, 5, 8)$.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2303.13906>)

[PDF](<https://arxiv.org/pdf/2303.13906.pdf>)