Bounds on Regularity of Quadratic Monomial Ideals

2019/06/14 by Blekherman, Grigoriy, Jung, Jaewoo
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.06358

Abstract

Castelnuovo-Mumford regularity is a measure of algebraic complexity of an ideal. Regularity of monomial ideals can be investigated combinatorially. We use a simple graph decomposition and results from structural graph theory to prove, improve and generalize many of the known bounds on regularity of quadratic square-free monomial ideals.

Related

• Regularity of squarefree monomial ideals
• Linearly presented modules and bounds on the Castelnuovo-Mumford regularity of ideals
• Bounds on the regularity and projective dimension of ideals associated to graphs
• Characteristic-free bounds for the Castelnuovo–Mumford regularity
• Regularity of Edge Ideals and Their Powers