A Variant of IdentityFinder and Some New Identities of Rogers–Ramanujan–MacMahon Type

We report on findings of a variant of 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 an...

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Bibliographic Details
Published in:Annals of combinatorics 2019-11, Vol.23 (3-4), p.807-834
Main Authors: Kanade, Shashank, Nandi, Debajyoti, Russell, Matthew C.
Format: Article
Language:English
Subjects:
Combinatorics
Mathematics
Mathematics and Statistics
Parameterization
Partitions (mathematics)
Searching
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Summary:We report on findings of a variant of 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.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-019-00474-3