Linearity defect of edge ideals and Fröberg's theorem

DOI10.1007/s10801-015-0662-6zbMath1342.05064arXiv1506.05769OpenAlexW3103085502MaRDI QIDQ737978

Thanh Vu, Dang Hop Nguyen

Publication date: 12 August 2016

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05769

zbMATH Keywords

Castelnuovo-Mumford regularityedge ideallinearity defectweakly chordal graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Simplicial sets and complexes in algebraic topology (55U10) Other special types of modules and ideals in commutative rings (13C13) Local rings and semilocal rings (13H99)

Related Items (9)

Survey on Regularity of Symbolic Powers of an Edge Ideal ⋮ On some algebraic properties of edge ideals of ladder graphs ⋮ Comparison between regularity of small symbolic powers and ordinary powers of an edge ideal ⋮ Induced matchings in strongly biconvex graphs and some algebraic applications ⋮ Nonvanishing Betti numbers of edge ideals of weakly chordal graphs ⋮ Powers of sums and their homological invariants ⋮ The absolutely Koszul property of Veronese subrings and Segre products ⋮ Regularity and Koszul property of symbolic powers of monomial ideals ⋮ Betti numbers of fat forests and their Alexander dual

Uses Software

• Macaulay2
• LinearityDefect

Cites Work

• Notes on the linearity defect and applications
• Matchings, coverings, and Castelnuovo-Mumford regularity
• Regularity and linearity defect of modules over local rings
• Progress in commutative algebra 1. Combinatorics and homology
• Intersections of Leray complexes and regularity of monomial ideals
• Splittable ideals and the resolutions of monomial ideals
• Algebraic properties of edge ideals via combinatorial topology
• Finitely presented graded Lie algebras and homomorphisms of local rings
• The lcm-lattice in monomial resolutions
• Optimizing weakly triangulated graphs
• Algorithms for weakly triangulated graphs
• Regularity 3 in edge ideals associated to bipartite graphs
• Characteristic-independence of Betti numbers of graph ideals
• Linearity defects of face rings
• On the linearity defect of the residue field
• Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
• Koszul modules
• Linearity defects of modules over commutative rings
• Non-vanishingness of Betti Numbers of Edge Ideals
• Frames and degenerations of monomial resolutions
• Splittings of monomial ideals
• Restricting linear syzygies: algebra and geometry
• Componentwise linear ideals
• Sheaf cohomology and free resolutions over exterior algebras
• Monomial Ideals
• A Beginner’s Guide to Edge and Cover Ideals
• Regularity of Squarefree Monomial Ideals
• Regularity and projective dimension of the edge ideal of $C_5$-free vertex decomposable graphs
• Dependence of Betti Numbers on Characteristic
• The possible extremal Betti numbers of a homogeneous ideal
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