ON SOME COMBINATORIAL INTERPRETATIONS FOR ROGERS-RAMANUJAN TYPE IDENTITIES
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 554
DOI: https://doi.org/10.56827/SEAJMMS.2023.1901.1
Author :
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)
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 overpartitions; Split part $n$--color partition; $2$--color $F$--partition; Modular Ferrers diagram; Combinatorial interpretation.
A.M.S. subject classification
05A17, 19, 11P81, 84.
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