A variant of ${\texttt{IdentityFinder}}$ and some new identities of Rogers-Ramanujan-MacMahon type
Shashank Kanade, Debajyoti Nandi, Matthew C. Russell

TL;DR
This paper introduces a modified version of the IdentityFinder program, incorporating algebraic mechanisms, to discover and prove new Rogers-Ramanujan-MacMahon type identities by excluding certain partitions.
Contribution
A novel variant of IdentityFinder that leverages algebraic insights to identify and prove new partition identities of Rogers-Ramanujan-MacMahon type.
Findings
Several new identities of Rogers-Ramanujan-MacMahon type discovered.
The modified program successfully proves the new identities.
Enhanced understanding of partition restrictions and algebraic mechanisms.
Abstract
We report on findings of a variant of - a Maple program that was used by two of the authors to conjecture several new identities of Rogers-Ramanujan kind. In the present search, we modify the parametrization of the search space by taking into consideration several aspects of Lepowsky and Wilson's -algebraic mechanism and its variant by Meurman and Primc. We search for identities based on forbidding the appearance of "flat" partitions as sub-partitions. Several new identities of Rogers-Ramanujan-MacMahon type are found and proved.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research
