2023/04/23 by Ajay Kumar, Bijender, Kumar, Ajay
Computer Science · Mathematics · #05E40 #13C14 #13D02 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2304.11640
openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a simplicial complex Δ, we investigate how to construct a new simplicial complex Δ such that the corresponding monomial ideals satisfy nice algebraic properties. We give a procedure to check the vertex decomposability of an arbitrary hypergraph. As a consequence, we prove that attaching non-pure skeletons at all vertices of a cycle cover of a simplicial complex Δ results in a simplicial complex Δ such that the associated hypergraph H(Δ) is vertex decomposable. Also, we prove that all symbolic powers of the cover ideal of Δ are componentwise linear. Our work generalizes the earlier known result where non-pure complete graphs were added to all vertices of a cycle cover of a graph.