2018/04/16 by Kuei-Nuan Lin, Lin, Kuei-Nuan, Sonja Mapes +1
Computer Science · Mathematics · #05E40 #13D02 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1804.05919
openalex publication_date 2018/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a square-free monomial ideal I in a polynomial ring R over a field \mathbbK, one can associate it with its LCM-lattice and its hypergraph. In this short note, we establish the connection between the LCM-lattice and the hypergraph, and in doing so we provide a sufficient condition for removing higher dimension edges of the hypergraph without impacting the projective dimension of the square-free monomial ideal. We also offer algorithms to compute the projective dimension of a class of square-free monomial ideals built using the new result and previous results of Lin-Mantero.