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Multidimensional Rogers-Ramanujan type identities with parameters

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arxiv 2302.00357 v3 pith:YTTNRUYC submitted 2023-02-01 math.CO

Chuanan Wei , Yuanbo Yu , Guozhu Ruan This is my paper · ORCID
classification math.CO
keywords parametersidentitiesmultidimensionalresultsseriestypewangberkovich
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Via the contour integral method, we establish a reduction formula from a double series to a single series with parameters, which not only implies Uncu and Zudilin's two results and Cao and Wang's two results, but also is related to Berkovich and Warnaar's equation. Similarly, we also discover some triple-sum generalizations of Cao and Wang's formulas. As conclusions, several multidimensional Rogers--Ramanujan type identities with parameters or without parameters are given.

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  1. The combinatorics of identities involving overpartitions with distinct parts

    math.CO 2025-06 conditional novelty 5.0 of 10

    New part-counting refinements of Andrews and El Bachraoui's overpartition identities are derived analytically, with bijective proofs supplied for several of the identities.

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