On Stanley-Reisner Rings with Minimal Betti Numbers
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915892725547008 |
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| author | Dai, Pimeng Yu, Li |
| author_facet | Dai, Pimeng Yu, Li |
| contents | We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal possible Betti numbers. We find that these simplicial complexes have very special combinatorial and topological structures. For example, the Betti numbers of their Stanley-Reisner rings are given by the binomial coefficients, and their full subcomplexes are homotopy equivalent either to a point or to a sphere. These properties make it possible for us to either classify them or construct them inductively from instances with fewer vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25540 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Stanley-Reisner Rings with Minimal Betti Numbers Dai, Pimeng Yu, Li Commutative Algebra Algebraic Topology Combinatorics 13F55, 13D02, 05E40, 05E45 We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal possible Betti numbers. We find that these simplicial complexes have very special combinatorial and topological structures. For example, the Betti numbers of their Stanley-Reisner rings are given by the binomial coefficients, and their full subcomplexes are homotopy equivalent either to a point or to a sphere. These properties make it possible for us to either classify them or construct them inductively from instances with fewer vertices. |
| title | On Stanley-Reisner Rings with Minimal Betti Numbers |
| topic | Commutative Algebra Algebraic Topology Combinatorics 13F55, 13D02, 05E40, 05E45 |
| url | https://arxiv.org/abs/2603.25540 |