Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.12945 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910705624547328 |
|---|---|
| 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 |