Pure Simplicial and Clique Complexes with a Fixed Number of Facets
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910705624547328 |
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| author | Betre, Kassahun H Zhang, Yan X Edmond, Carter |
| author_facet | Betre, Kassahun H Zhang, Yan X Edmond, Carter |
| contents | We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a clique complex that depends only on the list of facets. We also prove a theorem that a class of ``triangle-intersection free" pure clique complexes are uniquely determined up to isomorphism merely from the facet-adjacency matrix. Lastly, we count the number of pure simplicial complexes with a fixed number of facets and find an upper bound to the number of pure clique complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pure Simplicial and Clique Complexes with a Fixed Number of Facets Betre, Kassahun H Zhang, Yan X Edmond, Carter Combinatorics We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a clique complex that depends only on the list of facets. We also prove a theorem that a class of ``triangle-intersection free" pure clique complexes are uniquely determined up to isomorphism merely from the facet-adjacency matrix. Lastly, we count the number of pure simplicial complexes with a fixed number of facets and find an upper bound to the number of pure clique complexes. |
| title | Pure Simplicial and Clique Complexes with a Fixed Number of Facets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.12945 |