Chordality of clutters with vertex decomposable dual and ascent of clutters

DOI10.1016/j.jcta.2019.06.007zbMath1421.05101arXiv1708.07372OpenAlexW2748150495MaRDI QIDQ2326332

Ashkan Nikseresht

Publication date: 7 October 2019

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

Full work available at URL: https://arxiv.org/abs/1708.07372

zbMATH Keywords

linear resolutionsquarefree monomial idealchordal cluttervertex decomposable simplicial complexascent of a clutter

Mathematics Subject Classification ID

Cohen-Macaulay modules (13C14) Combinatorial aspects of simplicial complexes (05E45)

Related Items (10)

Deriving some properties of Stanley-Reisner rings from their squarefree zero-divisor graphs ⋮ Partition and Cohen-Macaulay extenders ⋮ On Gorenstein circulant graphs ⋮ Line graphs with a Cohen-Macaulay or Gorenstein clique complex ⋮ Gorenstein and Cohen–Macaulay matching complexes ⋮ Multigraded minimal free resolutions of simplicial subclutters ⋮ Trung's construction and the Charney-Davis conjecture ⋮ Non-ridge-chordal complexes whose clique complex has shellable Alexander dual ⋮ Chordality, \(d\)-collapsibility, and componentwise linear ideals ⋮ Completing and Extending Shellings of Vertex Decomposable Complexes

Cites Work

• Stability of Betti numbers under reduction processes: towards chordality of clutters
• Chordal and sequentially Cohen-Macaulay clutters
• Ideals with linear quotients
• Rings with monomial relations having linear resolutions
• Combinatorial properties of ``cleanness
• Extendable shellability for rank 3 matroid complexes
• A criterion for a monomial ideal to have a linear resolution in characteristic 2
• Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution
• Simplicial orders and chordality
• Decomposable clutters and a generalization of Simon's conjecture
• Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
• On Generalization of Cycles and Chordality to Clutters from an Algebraic Viewpoint
• Monomial Ideals

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