A variant of ${\texttt{IdentityFinder}}$ and some new identities of Rogers-Ramanujan-MacMahon type

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 ${\texttt{IdentityFinder}}$ - 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 $Z$-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.