A non-partitionable Cohen–Macaulay simplicial complex
A non-partitionable Cohen–Macaulay simplicial complex
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DOI：
10.1016/j.aim.2016.05.011
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发表时间：
2015-04
影响因子：
0.7
通讯作者：
Art M. Duval;Bennet Goeckner;Caroline J. Klivans;Jeremy L. Martin
中科院分区：
文献类型：
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作者：
Art M. Duval;Bennet Goeckner;Caroline J. Klivans;Jeremy L. Martin
Stanley的一个长期猜想指出，每个Cohen-Macaulay单纯复形都是可分的。我们通过构造一个明确的反例来反驳这个猜想。由于Herzog，Jahan和Yassemi的一个结果，我们的构造也证明了单项式理想的Stanley深度总是至少等于它的深度的猜想是错误的.
A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves the conjecture that the Stanley depth of a monomial ideal is always at least its depth.