Greedy Regular Convolutions

[2504.02795] Greedy Regular Convolutions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2504.02795 (math) [Submitted on 3 Apr 2025 ( v1 ), last revised 14 Aug 2026 (this version, v4)] Title: Greedy Regular Convolutions Authors: Jan Snellman View a PDF of the paper titled Greedy Regular Convolutions, by Jan Snellman View PDF HTML (experimental) Abstract: We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a common finite bound for the rank of primitive numbers. Among these "greedy convolutions" the unitary convolution and the "ternary convolution" are particularly interesting: they are the only regular, homogeneous convolutions where each primitive number have the same finite rank. While the greedy convolution of length 3, also described in detail, has primitive numbers of rank 3 and rank 1, it is still special in that the set of primitives can be generated by a simple recursive procedure that we name selective sifting. Comments: 34 pages, 9 figures. version of 2025-04-27: corrected characterisation of primitive elements (Lemma 14). version of 2025-04-29: typographic improvements, included biblatex files so proper bibliography could be processed. version of 2026-08-14: corrects typos: two strict inequality signs changed to nonstrict, letter p change to letter q, fraction 1/12 changed to 1/6 Subjects: Number Theory (math.NT) MSC classes: 11N25, 11A05, 05A18 Cite as: arXiv:2504.02795 [math.NT] (or arXiv:2504.02795v4 [math.NT] for this version) https://doi.org/10.48550/arXiv.2504.02795 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jan Snellman [ view email ] [v1] Thu, 3 Apr 2025 17:41:11 UTC (624 KB) [v2] Sun, 27 Apr 2025 08:54:05 UTC (603 KB) [v3] Tue, 29 Apr 2025 12:06:10 UTC (756 KB) [v4] Fri, 14 Aug 2026 18:19:02 UTC (1,590 KB) Full-text links: Access Paper: View a PDF of the paper titled Greedy Regular Convolutions, by Jan Snellman View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : Tn1.png Tn2.png Tn3.png Tn4.png errata_to_previous_version.tex explanation_of_ternary.org explanation_of_ternary.pdf he3.png length2distance.png length3blocks.png length3distance.png length4distance.png oeis.txt ternary_code.sage terse_explanation_of_ternary.org terse_explanation_of_ternary.pdf (11 additional files not shown) Current browse context: math.NT < prev | next > new | recent | 2025-04 Change to browse by: math 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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