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Title
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Skeletons of monomial ideals
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Type
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JournalPaper
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Keywords
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Monomial ideals;depth;skeleton;Cohen−Macaulay;Stanley decompositions
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Abstract
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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
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Researchers
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Xinxian Zheng (Third Researcher), Ali Soleyman Jahan (Second Researcher), Jurgen Herzog (First Researcher)
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