Abstract
Let \(pod_3(n)\) denote the number of 3-regular partitions with distinct odd parts (and even parts are unrestricted) of a non-negative integer n. In this paper, we present infinite families of Ramanujan-type congruences modulo 2 and 3 for \(pod_3(n)\).
Similar content being viewed by others
References
Berndt, B.C.: Ramanujan’s Notebooks, Part III. Springer, New York (1991)
Cui, S.P., Gu, N.S.S.: Arithmetic properties of \({\ell }\)- regular partitions. Adv. Appl. Math. 51, 507–523 (2013)
Gireesh, D.S., Hirschhorn, M.D., Naika, M.S.M.: On 3-regular partitions with odd parts distinct. Ramanujan J. 44(1), 227–236 (2017)
HirschhornEmail, M.D., Sellers, J. A.: A congruence modulo 3 for partitions into distinct non-multiples of four. J. Int. Seq. 17(1), 1–7 (2014), Article 14.9.6
Xia, E.X.W., Yao, O.X.M.: Analogues of Ramanujans partition identities. Ramanujan J. 31, 373–396 (2013)
Acknowledgements
Author thanks the referees for his/her valuable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saikia, N. Infinite Families of Congruences for 3-Regular Partitions with Distinct Odd Parts. Commun. Math. Stat. 8, 443–451 (2020). https://doi.org/10.1007/s40304-019-00182-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40304-019-00182-7