Rank deviations for overpartitions

2023/07/07 by Jeremy Lovejoy, Robert Osburn, Lovejoy, Jeremy +1 · 1 citation
Mathematics · #05A17 #11F11 #11F27 #11F37 #11P83 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2307.03418

openalex publication_date 2023/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous overpartition rank difference identities in the literature. We give two illustrations.

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• Generalized rank deviations for overpartitions

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