On a 3-Way Combinatorial Identity

Garima Sood, Ashok Kumar Agarwal^*

Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India.

DOI: 10.4236/ojdm.2014.44012                

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.

Keywords

Basic Series, Partitions, N-Colour Partitions, Frobenius Partitions, Lattice Paths, Generating Functions, Combinatorial Identities

Conflicts of Interest

The authors declare no conflicts of interest.

References

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