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arXiv · 2411.12945

Pure Simplicial and Clique Complexes with a Fixed Number of Facets

Kassahun H Betre·Yan X Zhang·Carter Edmond
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Abstract

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.

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Kassahun H Betre, Yan X Zhang, Carter Edmond. 2024-11-20. Pure Simplicial and Clique Complexes with a Fixed Number of Facets. https://arxiv.org/abs/2411.12945

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