Skip to main content
SpringerLink
Log in

On the parity of broken \(k\)-diamond partitions

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

In this paper, we prove several new parity results for broken \(k\)-diamond partitions on certain types of arithmetic progressions. We also obtain bounds for the parity of broken \(k\)-diamond partitions and more general colored partitions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Andrews, G.E., Paule, P.: MacMahon’s partition analysis XI. Broken diamonds and modular forms. Acta Arith. 126, 281–294 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Andrews, G.E., Paule, P., Riese, A.: MacMahon’s partition analysis VIII. Plane partition diamonds. Adv. Appl. Math. 27, 231–242 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baruah, N.D., Sarmah, B.K.: Identities for self-conjugate 7- and 9-core partitions. Int. J. Number Theory 8, 653–667 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Berndt, B.C., Yee, A.J., Zaharescu, A.: On the parity of partition functions. Int. J. Math. 14, 437–459 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Berndt, B.C., Yee, A.J., Zaharescu, A.: New theorems on the parity of partition functions. J. Reine Angew. Math. 566, 91–109 (2004)

    MATH  MathSciNet  Google Scholar 

  6. Chan, S.H.: Some congruences for Andrews–Paule’s broken 2-diamond partitions. Discrete Math. 308, 5735–5741 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Garvan, F., Kim, D., Stanton, D.: Cranks and t-cores. Invent. Math. 101, 1–17 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hirschhorn, M.D.: An identity of Ramanujan, and applications. In: q-Series from a Contemporary Perspective. Contemporary Mathematics, vol. 254, pp. 229–234. American Mathematical Society, Providence, RI (2000)

  9. Hirschhorn, M.D., Sellers, J.A.: On recent congruence results of Andrews and Paule for broken \(k\)-diamonds. Bull. Aust. Math. Soc. 75, 121–126 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. MacMahon, P.A.: Combinatory Analysis. Cambridge University Press, Cambridge (1916)

    Google Scholar 

  11. Radu, S., Sellers, J.A.: Parity results for broken \(k\)-diamond partitions and \((2k+1)\)-cores. Acta Arith. 146, 43–52 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Radu, S.: An algorithmic approach to Ramanujan’s congruences. Ramanujan J. 20, 215–251 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the referees for their comments and suggestions, which led to a significant improvement of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL, 61801, USA

    Sneha Chaubey, Wei Cheng, Amita Malik & Alexandru Zaharescu

Authors
  1. Sneha Chaubey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amita Malik
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexandru Zaharescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sneha Chaubey.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chaubey, S., Cheng, W., Malik, A. et al. On the parity of broken \(k\)-diamond partitions. Ann Univ Ferrara 60, 347–361 (2014). https://doi.org/10.1007/s11565-014-0211-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-014-0211-6

Keywords

Mathematics Subject Classification (2010)

Search

Navigation