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On a 3-Way Combinatorial Identity
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India
- 1 Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India
- 2 Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India
Open Journal of Discrete Mathematics·Volume 04 (2014)·Pages 89–96·Published 30 September 2014·DOI10.4236/ojdm.2014.44012
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Abstract
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.
KeywordsBasic SeriesPartitionsN-Colour PartitionsFrobenius PartitionsLattice PathsGenerating FunctionsCombinatorial Identities
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