Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forests

DOI10.1007/s40840-020-01052-0OpenAlexW3118549010MaRDI QIDQ2045255

Jiaqi Zhang, Guangjun Zhu, Hong Wang, Li Xu

Publication date: 12 August 2021

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.03019

zbMATH Keywords

regularityprojective dimensionedge idealpowers of the edge idealvertex-weighted rooted forest

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Syzygies, resolutions, complexes and commutative rings (13D02) Directed graphs (digraphs), tournaments (05C20) Signed and weighted graphs (05C22) Combinatorial aspects of commutative algebra (05E40)

Related Items

Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests ⋮ Powers of edge ideals of weighted oriented graphs with linear resolutions ⋮ Algebraic properties of edge ideals of some vertex-weighted oriented \(m\)-partite graphs

Uses Software

• CoCoA

Cites Work

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• Depth and regularity of powers of sums of ideals
• Minimum distance functions of graded ideals and Reed-Muller-type codes
• Bounds on the regularity and projective dimension of ideals associated to graphs
• Path ideals of rooted trees and their graded Betti numbers
• Splittable ideals and the resolutions of monomial ideals
• A lower bound for depths of powers of edge ideals
• Regularity of powers of forests and cycles
• Minimal resolutions of some monomial ideals
• Regularity of powers of bipartite graphs
• Powers of sums and their homological invariants
• Cohen-Macaulay graphs
• The regularity of powers of edge ideals
• Regularity of edge ideals and their powers
• Monomial ideals of weighted oriented graphs
• Projective dimension and regularity of edge ideals of some weighted oriented graphs
• On the asymptotic linearity of Castelnuovo-Mumford regularity.
• The depth of powers of an ideal
• Betti Numbers of Path Ideals of Trees
• Regularity of powers of edge Ideal of whiskered cycles
• Splittings of monomial ideals
• Algebraic Properties of the Path Ideal of a Tree
• The asymptotic nature of the analytic spread
• Projective dimension and regularity of path ideals of cycles
• Graded Betti numbers of path ideals of cycles and lines
• Projective dimension and regularity of the path ideal of the line graph
• Asymptotic behaviour of Castelnuovo-Mumford regularity
• EDGE IDEALS OF WEIGHTED GRAPHS
• Monomial Ideals
• Regularity of bicyclic graphs and their powers
• Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs
• Regularity of Squarefree Monomial Ideals
• Depths of Powers of the Edge Ideal of a Tree
• HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS
• On the resolution of ideals of fat points