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}
}