Intersections of Leray complexes and regularity of monomial ideals

DOI10.1016/j.jcta.2006.01.005zbMath1105.13026arXivmath/0601745OpenAlexW2009820428MaRDI QIDQ855856

Roy Meshulam, Gil Kalai

Publication date: 7 December 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601745

zbMATH Keywords

regularitymonomial idealssimplicial homology

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55)

Related Items (33)

Leray numbers of complexes of graphs with bounded matching number ⋮ Stanley depth and Stanley support-regularity of monomial ideals ⋮ Some algebraic Invariants of the residue class rings of the edge ideals of perfect semiregular trees ⋮ A Generalization of the Taylor Complex Construction ⋮ Edge ideals of squares of trees ⋮ Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry ⋮ The edge ideal of a graph and its splitting graphs ⋮ Regularity of powers of edge ideals of some graphs ⋮ RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES ⋮ On the Castelnuovo-Mumford regularity of squarefree powers of edge ideals ⋮ Results on the regularity of square-free monomial ideals ⋮ Matchings, coverings, and Castelnuovo-Mumford regularity ⋮ Topology of complements of skeletons ⋮ Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes ⋮ Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters ⋮ The regularity of almost all edge ideals ⋮ Noncover complexes, independence complexes, and domination numbers of hypergraphs ⋮ The intersection of a matroid and an oriented matroid ⋮ Homological invariants of the Stanley–Reisner ring of a k-decomposable simplicial complex ⋮ Leray numbers of projections and a topological Helly-type theorem ⋮ Helly numbers of acyclic families ⋮ Domination numbers and noncover complexes of hypergraphs ⋮ On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces ⋮ Improved bounds for the regularity of edge ideals of graphs ⋮ The \(v\)-number of edge ideals ⋮ Dominating induced matchings of finite graphs and regularity of edge ideals ⋮ Collapsibility of non-cover complexes of graphs ⋮ Regularity of bicyclic graphs and their powers ⋮ Linearity defect of edge ideals and Fröberg's theorem ⋮ Higher chordality: From graphs to complexes ⋮ Cooperative conditions for the existence of rainbow matchings ⋮ Dimension gaps between representability and collapsibility ⋮ Bounds for the regularity of product of edge ideals

Cites Work

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• A topological colorful Helly theorem
• d-collapsing and nerves of families of convex sets
• Transversal numbers for hypergraphs arising in geometry
• Topology of plane arrangements and their complements
• The Geometry of Syzygies

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