ON SOME COMBINATORIAL INTERPRETATIONS FOR ROGERS-RAMANUJAN TYPE IDENTITIES

V Gupta; M Rana

doi:10.56827/SEAJMMS.2023.1901.1

V Gupta School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, Punjab, INDIA
M Rana School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, Punjab, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2023.1901.1

Keywords: Rogers–Ramanujan type identities; n–color overpartitions; Split part n–color partition; 2–color F–partition; Modular Ferrers diagram; Combinatorial interpretation.

Abstract

We implement an advanced technique to provide combinatorial interpretations of some Rogers–Ramanujan type identities, also known as sum–product identities. Specifically, we elaborate on the notion of modular Ferrers diagrams to explain these identities in terms of n–color overpartitions. Additionally, we reveal the interdependence between split part n–color partitions, 2–color F–partitions, and n–color overpartitions.