Convex Geometry of Building Sets
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914148179247104 |
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| author | Backman, Spencer Danner, Richard |
| author_facet | Backman, Spencer Danner, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex Geometry of Building Sets Backman, Spencer Danner, Richard Combinatorics Algebraic Geometry 06A07, 05B35, 52C35 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. |
| title | Convex Geometry of Building Sets |
| topic | Combinatorics Algebraic Geometry 06A07, 05B35, 52C35 |
| url | https://arxiv.org/abs/2403.05514 |