Skeletons of monomial ideals |
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| Authors: | Jürgen Herzog Ali Soleyman Jahan Xinxian Zheng |
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| Institution: | Fachbereich Mathematik und Informatik, Universit?t Duisburg‐Essen, Campus Essen, 45117 Essen, Germany |
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| Abstract: | In analogy to the skeletons of a simplicial complex and their Stanley–Reisner ideals we introduce the skeletons of an arbitrary monomial ideal I ? S = K x1, …, xn ]. This allows us to compute the depth of S /I in terms of its skeleton ideals. We apply these techniques to show that Stanley's conjecture on Stanley decompositions of S /I holds provided it holds whenever S /I is Cohen–Macaulay. We also discuss a conjecture of Soleyman Jahan and show that it suffices to prove his conjecture for monomial ideals with linear resolution (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Monomial ideals depth skeleton Cohen− Macaulay Stanley decompositions |
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