On Generalization of Cycles and Chordality to Clutters from an Algebraic Viewpoint

• 来源期刊: 代数集刊（英文版）
• 关键词: chordal clutter squarefree monomial ideal linear resolution cycle simplicial complex
• 年，卷（期）: 2017,（4）
• 页码范围: 611-624
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386717000402

摘要

In this paper,we study the notion of chordality and cycles in clutters from a commutative algebraic point of view.The corresponding concept of chordality in commutative algebra is having a linear resolution.We mainly consider the generalization of chordality proposed by Bigdeli et al.in 2017 and the concept of cycles introduced by Cannon and Faridi in 2013,and study their interrelations and algebraic interpretations.In particular,we investigate the relationship between chordality and having linear quotients in some classes of clutters.Also,we show that if ee is a clutter such that <e> is a vertex decomposable simplicial complex or I(e) is squarefree stable,then e is chordal.