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.Comment: 13 pages, final version to appear in J. Comm. Al