On a New Class of Combinatorial Identities

Abstract

In this paper, we interpret a generalized basic series as the generating function of two different combinatorial objects, viz., a restricted \(n\)-colour partition function, which we call a two-colour partition function, and a weighted lattice path function. This leads to infinitely many combinatorial identities. Our main result has the potential of yielding many Rogers-Ramanujan-MacMahon type combinatorial identities. This is illustrated by an example.