Monomial polarization and depolarization of abstract simplicial complexes

Monomial polarization and depolarization of abstract simplicial complexes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Monomial polarization and depolarization of abstract simplicial complexes Víctor M. López-Antón, Pablo Munarriz-Senosiain, Patricia Pascual-Ortigosa, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7214042/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Apr, 2026 Read the published version in Mediterranean Journal of Mathematics → Version 1 posted 7 You are reading this latest preprint version Abstract We translate the operations of polarization and depolarization from monomial ideals in a polynomial ring to abstract simplicial complexes. As a result, we explicitly describe the relation between the Koszul simplicial complex of a monomial ideal and that of its polarization. Using the simplicial translation of depolarization we propose a way to reduce a simplicial complex to a smaller one with the same homology. This type of reduction, that can be interpreted as non-elementary collapse, can be used as a pre-process step for algorithms on simplicial complexes. We apply this methodology to the efficient computation of the Alexander dual of abstract simplicial complexes. Simplicial complexes polarization depolarization Koszul simplicial complex Stanley-Reisner rings Alexander dual Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 07 Apr, 2026 Read the published version in Mediterranean Journal of Mathematics → Version 1 posted Editorial decision: Revision requested 01 Dec, 2025 Reviews received at journal 19 Nov, 2025 Reviewers agreed at journal 01 Sep, 2025 Reviewers invited by journal 28 Aug, 2025 Editor assigned by journal 19 Aug, 2025 Submission checks completed at journal 27 Jul, 2025 First submitted to journal 25 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7214042","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":508307515,"identity":"9df3fdc6-0262-48e7-aa20-0a27ad3b2e77","order_by":0,"name":"Víctor M. 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