Combinatorial Interpretation of a Generalized Basic Series

A. K. Agarwal () and M. Rana ()
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A. K. Agarwal: Panjab University, Center for Advanced Study in Mathematics
M. Rana: Thapar University, School of Mathematics and Computer Applications

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 215-225 from Springer

Abstract: 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.

Keywords: Basal Serum; Combinatorial Identities; Infinite Family; Main Result; Bijection (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_7

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DOI: 10.1007/978-1-4939-0258-3_7

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