Lattices and hypergraphs associated to square-free monomial ideals. Issue 11 (19th August 2022)

• Record Type: Journal Article
• Authors: Lin, Kuei-Nuan; Mapes, Sonja
• Is Part Of: Communications in algebra. Volume 50:Issue 11(2022)
• Page Start: 4710
• Page End: 4724
• Publication Date: 2022-08-19
• Subjects: Hypergraphs -- lattices -- monomial ideals -- projective dimension; 13D02 -- 05E40; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2072853
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Given a square-free monomial ideal I in a polynomial ring R over a field K, 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.