Shashank Kanade, Matthew C. Russell
Published 2014-11-19Version 1
The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form) are typically of the form "product side" equals "sum side," with the product side enumerating partitions obeying certain congruence conditions and the sum side obeying certain initial conditions and difference conditions (along with possibly other restrictions). We use symbolic computation to generate various such sum sides and then use Euler's algorithm to see which of them actually do produce elegant conjectured product sides. We not only rediscover many of the known identities but also discover some apparently new ones, as conjectures supported by strong mathematical evidence.
A variant of ${\texttt{IdentityFinder}}$ and some new identities of Rogers-Ramanujan-MacMahon type
Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
Combinatorial proofs for identities related with generalizations of the mock theta functions $ω(q)$ and $ν(q)$
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