Skip to main content
SpringerLink
Log in

On an extension of a combinatorial identity

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript

Abstract

Using Frobenius partitions we extend the main results of [4]. This leads to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of Göllnitz-Gordon identities.

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

Similar content being viewed by others

References

  1. Agarwal A K, On a generalized partition theorem, J. Indian Math. Soc. 50 (1986) 185–190

    MATH  MathSciNet  Google Scholar 

  2. Agarwal A K and Andrews G E, Rogers-Ramanujan identities for partitions with N copies of N, J. Combin. Theory A45(1) (1987) 40–49

    Article  MathSciNet  Google Scholar 

  3. Agarwal A K and Bressoud D M., Lattice paths and multiple basic hypergeometric series, Pacific J. Math. 136(2) (1989) 209–228

    MATH  MathSciNet  Google Scholar 

  4. Agarwal A K and Rana M, New combinatorial versions of Göllnitz-Gordon identities, Utilitas Math. (to appear)

  5. Andrews, G E, The theory of partitions, Encyclopedia of mathematics and its applications, vol. 2 (Addison-Wesley) (1976)

  6. Andrews G E, Generalized Frobenius Partitions, Mem. Amer. Math. Soc. 49 (1984) 301, iv+44 pp.

    Google Scholar 

  7. Göllnitz H, Einfache partitionen (unpublished), Diplomarbeit, W.S. (1960) (Gotttingen) 65 pp.

  8. Göllnitz H, Partitionen mit Differenzenbedingungen, J. Reine Angew. Math. 225 (1967) 154–190

    MATH  MathSciNet  Google Scholar 

  9. Gordon B, Some continued fractions of the Rogers-Ramanujan type, Duke J. Math. 32 (1965) 741–748

    Article  MATH  Google Scholar 

  10. Slater L J, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952) 147–167

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Advanced Study in Mathematics, Panjab University, Chandigarh, 160 014, India

    M. Rana & A. K. Agarwal

Authors
  1. M. Rana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. K. Agarwal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rana, M., Agarwal, A.K. On an extension of a combinatorial identity. Proc Math Sci 119, 1–7 (2009). https://doi.org/10.1007/s12044-009-0001-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12044-009-0001-8

Keywords

Search

Navigation