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Stanley decompositions and partitionable simplicial complexes |
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| Authors: | Jürgen Herzog Ali Soleyman Jahan Siamak Yassemi |
| Institution: | 1.Fachbereich Mathematik und Informatik,Universit?t Duisburg-Essen,Essen,Germany;2.Department of Mathematics,University of Tehran,Tehran,Iran;3.Institute for Theoretical Physics and Mathematics (IPM),Tehran,Iran |
| Abstract: | We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen–Macaulay simplicial complexes. We also prove these conjectures for all Cohen–Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3. Dedicated to Takayuki Hibi on the occasion of his fiftieth birthday. |
| Keywords: | Stanley decompositions Partitionable simplicial complexes Pretty clean modules |
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