2024/11/20 by Kassahun Betre, Yan X Zhang, Betre, Kassahun H +2
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2411.12945
openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.