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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