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On a 3-Way Combinatorial Identity

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Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial identities. Using Frobenius partitions, we in this paper extend the result of [1] and obtain an infinite family of 3-way combinatorial identities. We illustrate by an example that our main result has a potential of yielding Rogers-Ramanujan-MacMahon type identities with convolution property.
Cite this paper
Sood, G. and Agarwal, A. (2014) On a 3-Way Combinatorial Identity. Open Journal of Discrete Mathematics, 4, 89-96. doi: 10.4236/ojdm.2014.44012. 
 
 

[1] Goyal, M. and Agarwal, A.K. On a New Class of Combinatorial Identities. ARS Combinatoria. (to appear).
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[3] MacMohan, P.A. (1916) Combinatory Analysis. Vol. 2, Cambridge University Press, London and New York.
[4] Göllnitz, H. (1960) Einfache Partitionen. Diplomarbeit W.S., Gotttingen, 65 p. (unpublished)
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[10] Subbarao, M.V. (1985) Some Rogers-Ramanujan Type Partition Theorems. Pacific Journal of Mathematics, 120, 431-435.
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http://dx.doi.org/10.1112/plms/s2-54.2.147                 eww141007lx
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