2008/03/10 by Huy Tai Ha, Huy Tài Hà, Ha, Huy Tai +4
Mathematics · #05C65 #05C75 #13F55 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.CO #msc:05C65 #msc:05C75 #msc:13F55
paper · pdf · doi:10.48550/arxiv.0803.1332
13 pages, final version to appear in J. Comm. Alg
arxiv created 2008/03/10 · openalex publication_date 2008/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.