Complementary vectors of simplicial complexes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908342807429120 |
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| author | Larson, Matt Stapledon, Alan |
| author_facet | Larson, Matt Stapledon, Alan |
| contents | We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley-Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complementary vectors of simplicial complexes Larson, Matt Stapledon, Alan Combinatorics Commutative Algebra 13F55 05E45 We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley-Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes. |
| title | Complementary vectors of simplicial complexes |
| topic | Combinatorics Commutative Algebra 13F55 05E45 |
| url | https://arxiv.org/abs/2504.20264 |