English

Depth of the 3-path Ideal of Square of a Path

Commutative Algebra 2025-07-14 v1

Abstract

In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2 n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path.

Keywords

Cite

@article{arxiv.2507.08516,
  title  = {Depth of the 3-path Ideal of Square of a Path},
  author = {Liuqing Yang and Lizhong Chu},
  journal= {arXiv preprint arXiv:2507.08516},
  year   = {2025}
}