Monomial ideals whose all matching powers are Cohen-Macaulay
Commutative Algebra
2025-04-25 v2 Combinatorics
Abstract
In the present paper, we aim to classify monomial ideals whose all matching powers are Cohen-Macaulay. We especially focus our attention on edge ideals. The Cohen-Macaulayness of the last matching power of an edge ideal is characterized, providing an algebraic analogue of the famous Tutte theorem regarding graphs having a perfect matching. For chordal graphs, very well-covered graphs and Cameron-Walker graphs, we completely solve our problem.
Cite
@article{arxiv.2410.01666,
title = {Monomial ideals whose all matching powers are Cohen-Macaulay},
author = {Antonino Ficarra and Somayeh Moradi},
journal= {arXiv preprint arXiv:2410.01666},
year = {2025}
}