Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Klivans Caroline J.

A non-partitionable Cohen–Macaulay simplicial complex
Art M. Duval  1  , Bennet Goeckner  2  , Caroline J. Klivans  3  , Jeremy Martin  2@  
1 : University of Texas [El Paso]  (UTEP)  -  Website
500 W University Ave, El Paso, TX 79968, États-Unis -  États-Unis
2 : Department of Mathematics [Kansas]  -  Website
Department of Mathematics Kansas State University Manhattan -  États-Unis
3 : Department of Mathematics
Brown University 151 Thayer Street Providence, RI 02912 USA -  États-Unis

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. 

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