Skip to main content
Log in

Infinite Families of Congruences for 3-Regular Partitions with Distinct Odd Parts

  • Published:
Communications in Mathematics and Statistics Aims and scope Submit manuscript

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 \(pod_3(n)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berndt, B.C.: Ramanujan’s Notebooks, Part III. Springer, New York (1991)

    Book  Google Scholar 

  2. Cui, S.P., Gu, N.S.S.: Arithmetic properties of \({\ell }\)- regular partitions. Adv. Appl. Math. 51, 507–523 (2013)

    Article  MathSciNet  Google Scholar 

  3. 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)

    Article  MathSciNet  Google Scholar 

  4. 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

  5. Xia, E.X.W., Yao, O.X.M.: Analogues of Ramanujans partition identities. Ramanujan J. 31, 373–396 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Author thanks the referees for his/her valuable comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nipen Saikia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40304-019-00182-7

Keywords

Mathematics Subject Classification

Navigation