2021/10/23 by Mohammad Farrokhi Derakhshandeh Ghouchan, Ghouchan, Mohammad Farrokhi Derakhshandeh, Alireza Shamsian +3
Computer Science · Mathematics · #05E45 (Primary) 05C65 (Secondary) #13F55 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2110.12170
openalex publication_date 2021/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an arbitrary hypergraph H, we may glue to H a family of hypergraphs to get a new hypergraph H' having H as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph H' is under control in terms of the glued components. This enables us to construct broad classes of simplicial complexes containing a given simplicial complex as induced subcomplex satisfying nice topological and combinatorial properties. Our results will be accompanied with some interesting open problems.