Depths and Cohen-Macaulay properties of path ideals

DOI10.1016/j.jpaa.2013.12.005zbMath1283.05271arXiv1211.4647OpenAlexW2085239953MaRDI QIDQ2439314

Yanyan Li

Publication date: 14 March 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4647

zbMATH Keywords

square-free monomial ideal

Mathematics Subject Classification ID

Trees (05C05) Hypergraphs (05C65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Ideals and multiplicative ideal theory in commutative rings (13A15) Cohen-Macaulay modules (13C14) Combinatorial aspects of commutative algebra (05E40)

Related Items (5)

Closed neighborhood ideals of finite simple graphs ⋮ On the matroidal path ideals ⋮ On the minimal path cover sets of union of certain graphs ⋮ Bounding the projective dimension of a squarefree monomial ideal via domination in clutters ⋮ Path ideals of weighted graphs

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Odd-cycle-free facet complexes and the König property
• Regularity, depth and arithmetic rank of bipartite edge ideals
• \(M\)-sequences, graph ideals, and ladder ideals of linear type
• On the ideal theory of graphs
• The stable set of associated primes of the ideal of a graph
• Cohen-Macaulay properties of square-free monomial ideals
• Cohen-Macaulay graphs
• Simplicial trees are sequentially Cohen-Macaulay
• Associated primes of powers of edge ideals
• The depth of powers of an ideal
• Standard graded vertex cover algebras, cycles and leaves
• Algebraic Properties of the Path Ideal of a Tree
• A study of graded extremal rings and of monominal rings.
• Depths of Powers of the Edge Ideal of a Tree

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