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Combinatorial Interpretation of a Generalized Basic Series

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Analytic Number Theory, Approximation Theory, and Special Functions

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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.

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Acknowledgements

The first author is an emeritus scientist of the Council of Scientific and Industrial Research (CSIR), Government of India. He was supported by CSIR Research Scheme No. 21(0879)/11/EMR-II.

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Authors and Affiliations

  1. Center for Advanced Study in Mathematics, Panjab University, Chandigarh, 160014, India

    A. K. Agarwal

  2. School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab, India

    M. Rana

Authors
  1. A. K. Agarwal
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  2. M. Rana
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Correspondence to A. K. Agarwal .

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Editors and Affiliations

  1. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

Additional information

Dedicated to Professor Hari M. Srivastava

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Agarwal, A.K., Rana, M. (2014). Combinatorial Interpretation of a Generalized Basic Series. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_7

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