Cohen-Macaulay admissible clutters

Details Cohen-Macaulay admissible clutters Cohen-Macaulay admissible clutters

2008-03-10

arxiv.org/abs/0803.1332v1

Mathematics

Commutative Algebra

13 pages, final version to appear in J. Comm. Alg

Scientific paper

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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