TITLE:
On a 3-Way Combinatorial Identity
AUTHORS:
Garima Sood, Ashok Kumar Agarwal
KEYWORDS:
Basic Series, Partitions, N-Colour Partitions, Frobenius Partitions, Lattice Paths, Generating Functions, Combinatorial Identities
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.4 No.4,
September
30,
2014
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.