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RSMAMS SEAJMAMS South East Asian Journal of Mathematics and Mathematical Sciences
Home Volume 19, Issue 1 Article
Research Article

ON SOME COMBINATORIAL INTERPRETATIONS FOR ROGERS-RAMANUJAN TYPE IDENTITIES

V
V. Gupta School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, Punjab, INDIA
M
M. Rana School of Mathematics, Thapar Institute of Engineering and Technology, Patiala - 147004, Punjab, INDIA
Volume 19, Issue 1 Pages 1-16 April 30, 2023 785 downloads
Article overview

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.

Keywords and Phrases

Rogers--Ramanujan type identities$n$--color overpartitionsSplit part $n$--color partition$2$--color $F$--partitionModular Ferrers diagramCombinatorial interpretation.

AMS Subject Classification

05A17, 19, 11P81, 84.

Reference information

How to Cite

V. Gupta, M. Rana (2023). ON SOME COMBINATORIAL INTERPRETATIONS FOR ROGERS-RAMANUJAN TYPE IDENTITIES. South East Asian Journal of Mathematics and Mathematical Sciences, 19(1), 1-16.
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