Two lower bounds for the Stanley depth of monomial ideals |
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| Authors: | L Katthän S A Seyed Fakhari |
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| Affiliation: | 1. Universit?t Osnabrück, FB Mathematik/Informatik, Osnabrück, Germany;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran |
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| Abstract: | Let  be two monomial ideals of the polynomial ring  . In this paper, we provide two lower bounds for the Stanley depth of  . On the one hand, we introduce the notion of lcm number of  , denoted by  , and prove that the inequality  holds. On the other hand, we show that  , where  denotes the order dimension of the lcm lattice of  . We show that I and  satisfy Stanley's conjecture, if either the lcm number of I or the order dimension of the lcm lattice of I is small enough. Among other results, we also prove that the Stanley–Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture. |
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| Keywords: | Monomial ideal Stanley depth lcm number lcm lattice order dimension simplicial complex Primary: 13C15 05E99 Secondary: 13C13 |
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