Cohen-Macaulay admissible clutters
Commutative Algebra
2008-03-11 v1 Combinatorics
Abstract
There is a one-to-one correspondence between square-free monomial ideals and clutters, which are also known as simple hypergraphs. It was conjectured that unmixed admissible clutters are Cohen-Macaulay. We prove the conjecture for uniform admissible clutters of heights 2 and 3. For admissible clutters of greater heights, we give a family of examples to show that the conjecture may fail. When the height is 4, we give an additional condition under which unmixed admissible clutters are Cohen-Macaulay.
Keywords
Cite
@article{arxiv.0803.1332,
title = {Cohen-Macaulay admissible clutters},
author = {Huy Tai Ha and Susan Morey and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:0803.1332},
year = {2008}
}
Comments
13 pages, final version to appear in J. Comm. Alg