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Combinatorial Interpretation of a Generalized Basic Series

In: Analytic Number Theory, Approximation Theory, and Special Functions

Author

Listed:
  • A. K. Agarwal

    (Panjab University, Center for Advanced Study in Mathematics)

  • M. Rana

    (Thapar University, School of Mathematics and Computer Applications)

Abstract

Recently Goyal and Agarwal (ARS Combinatoria, to appear) have interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This resulted in an infinite family of combinatorial identities. Using a bijection between the Bender–Knuth matrices and the n-colour partitions established by the first author in Agarwal (ARS Combinatoria, 61, 97–117, 2001), in this paper we extend the main result of Goyal and Agarwal to a 3-way infinite family of combinatorial identities. We illustrate by two examples that our main result has the potential of yielding many Rogers–Ramanujan–MacMahon type combinatorial identities.

Suggested Citation

  • A. K. Agarwal & M. Rana, 2014. "Combinatorial Interpretation of a Generalized Basic Series," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 215-225, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_7
    DOI: 10.1007/978-1-4939-0258-3_7
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