Stability of Depths of Powers of Edge Ideals

Tran Nam Trung

doi:10.1016/j.jalgebra.2016.01.009

Stability of Depths of Powers of Edge Ideals

Commutative Algebra 2016-01-13 v1 Combinatorics

Authors: Tran Nam Trung

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit explicitly. This bound is always achieved if $G$ has no cycles of length $4$ and every its connected component is either a tree or a unicyclic graph.

Keywords

edge ideal depth powers of edge ideals stationary depth unicyclic graph tree

Cite

@article{arxiv.1601.02766,
  title  = {Stability of Depths of Powers of Edge Ideals},
  author = {Tran Nam Trung},
  journal= {arXiv preprint arXiv:1601.02766},
  year   = {2016}
}

Comments

To appear in Journal of Algebra

Related papers

View all related →