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arXiv · 0803.1332

Cohen-Macaulay admissible clutters

Huy Tai Ha·Susan Morey·Rafael H. Villarreal
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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.

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Huy Tai Ha, Susan Morey, Rafael H. Villarreal. 2008-03-10. Cohen-Macaulay admissible clutters. https://arxiv.org/abs/0803.1332

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