Möbius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications

[2608.14931] Möbius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2608.14931 (math) [Submitted on 14 Aug 2026] Title: Möbius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications Authors: Max A. Alekseyev View a PDF of the paper titled M\"obius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications, by Max A. Alekseyev View PDF HTML (experimental) Abstract: A coefficient duality first encountered for formal Bernoulli series is shown to be equivalent to a general Möbius covariance law for formal power series. We obtain a structural characterization, an eigenspace interpretation, and a weighted form of this duality. The Catalan convolution and Chebyshev identities from the motivating Bernoulli setting extend to arbitrary Möbius-covariant families and yield a general Ramanujan-type summation formula encompassing consecutive half-integer powers. The framework also recovers classical Bernoulli and Euler recurrences and produces recurrence families for colored matchings and generalized central trinomial coefficients, with further realizations from reflection-symmetric Appell sequences and Gorenstein Hilbert series. Subjects: Combinatorics (math.CO) ; Number Theory (math.NT) MSC classes: Primary 05A15, Secondary 11B68, 05A19, 33C45 ACM classes: G.2.1; I.1.4 Cite as: arXiv:2608.14931 [math.CO] (or arXiv:2608.14931v1 [math.CO] for this version) https://doi.org/10.48550/arXiv.2608.14931 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Max Alekseyev [ view email ] [v1] Fri, 14 Aug 2026 22:43:50 UTC (28 KB) Full-text links: Access Paper: View a PDF of the paper titled M\"obius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications, by Max A. Alekseyev View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2026-08 Change to browse by: math math.NT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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