2017/10/31 by Jorge Alberto Olarte, Jorge Olarte, Francisco Santos +2 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Boundary (topology) #Combinatorics #Commutative Algebra and Its Applications #Conjecture #Dimension (graph theory) #Flag (linear algebra) #Mathematical analysis #Mathematics #Property (philosophy) #Pure mathematics #Simplicial complex #Topological and Geometric Data Analysis #h-vector #math.CO #msc:05C35 #msc:05D05 #msc:05E45
paper · pdf · doi:10.1016/j.jcta.2019.105205
published as J. Combin. Th., Ser. A. 172 (May 2020), 105205 · 22 pages, v2: modified title and presentation, updated references, results unchanged
arxiv created 2018/04/16 · openalex publication_date 2020/01/14 · crossref created 2020/01/14 · crossref issued 2020/05/01 · crossref published 2020/05/01 · crossref published-print 2020/05/01 · arxiv updated 2020/08/25 · crossref deposited 2025/09/25 · crossref indexed 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that the family of facets of a pure simplicial complex of dimension up to three satisfies the Erdős-Ko-Rado property whenever it is flag and has no boundary ridges. We conjecture the same to be true in arbitrary dimension and give evidence for this conjecture. Our motivation is that complexes with these two properties include flag pseudo-manifolds and cluster complexes.