Convex Geometry of Building Sets

Mathematics > Combinatorics [Submitted on 8 Mar 2024 (v1), last revised 17 Jun 2026 (this version, v5)] Title:Convex Geometry of Building Sets View PDF HTML (experimental)Abstract:Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust combinatorial abstraction of convexity. Supersolvable convex geometries and antimatroids appear in the study of poset closure operators, Coxeter groups, and matroid activities. We prove that the building sets on a finite meet-semilattice form a supersolvable convex geometry. As an application, we demonstrate that building sets and nested set complexes respect certain restrictions of finite meet-semilattices unifying and extending results of several authors. Submission history From: Richard Danner [view email][v1] Fri, 8 Mar 2024 18:36:07 UTC (14 KB) [v2] Tue, 12 Mar 2024 13:06:48 UTC (16 KB) [v3] Wed, 26 Jun 2024 17:01:06 UTC (22 KB) [v4] Mon, 10 Nov 2025 23:49:35 UTC (21 KB) [v5] Wed, 17 Jun 2026 18:41:59 UTC (21 KB) Current browse context: math.CO References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) 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.