Lattices and hypergraphs associated to square-free monomial ideals

Kuei Nuan Lin*, Sonja Mapes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given a square-free monomial ideal I in a polynomial ring R over a field (Formula presented.) 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.

Original languageEnglish (US)
Pages (from-to)4710-4724
Number of pages15
JournalCommunications in Algebra
Volume50
Issue number11
DOIs
StatePublished - 2022

Keywords

  • Hypergraphs
  • lattices
  • monomial ideals
  • projective dimension

ASJC Scopus subject areas

  • Algebra and Number Theory

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