Constructions of Macaulay Posets and Macaulay Rings

[2502.15166] Constructions of Macaulay Posets and Macaulay Rings Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2502.15166 (math) [Submitted on 21 Feb 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Constructions of Macaulay Posets and Macaulay Rings Authors: Penelope Beall , Erenay Boyali , Nancy Chen , Ellen Chlachidze , Trong Toan Dao , Frederic Garvey , Mitchell Johnson , Yu Olivier Li , Nikola Kuzmanovski , Kelvin Ma , Treanungkur Mal , Rukshan Marasinghe Mudiyanselage , Quinlan Mayo , Nava Minsky-Primus , Alexandra Seceleanu , Sriram Veerapaneni View a PDF of the paper titled Constructions of Macaulay Posets and Macaulay Rings, by Penelope Beall and 15 other authors View PDF HTML (experimental) Abstract: A poset is Macaulay if its partial order and an additional total order interact well. Analogously, a ring is Macaulay if the partial order defined on its monomials by division interacts nicely with any total monomial order. We investigate methods of obtaining new structures through combining Macaulay rings and posets by means of certain operations inspired by topology. We examine whether these new structures retain the Macaulay property, identifying new classes of posets and rings for which the operations preserve the Macaulay property. Comments: Final version to appear in the Electronic Journal of Combinatorics Subjects: Combinatorics (math.CO) ; Commutative Algebra (math.AC) MSC classes: 05E40, 06A07, 06A11, 05D05, 13F55 Cite as: arXiv:2502.15166 [math.CO] (or arXiv:2502.15166v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2502.15166 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alexandra Seceleanu [ view email ] [v1] Fri, 21 Feb 2025 03:04:11 UTC (237 KB) [v2] Sat, 11 Apr 2026 20:07:40 UTC (188 KB) Full-text links: Access Paper: View a PDF of the paper titled Constructions of Macaulay Posets and Macaulay Rings, by Penelope Beall and 15 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2025-02 Change to browse by: math math.AC 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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