Stanley depth and the lcm-lattice
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Other documents of the author: Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José
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comunitat-uji-handle3:10234/8635
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Title
Stanley depth and the lcm-latticeDate
2017-08Publisher
ElsevierBibliographic citation
ICHIM, Bogdan; KATTHÄN, Lukas; MOYANO-FERNÁNDEZ, Julio José. Stanley depth and the lcm-lattice. Journal of Combinatorial Theory, Series A, 2017, vol. 150, p. 295-322.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0097316517300328Version
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Abstract
In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients of monomial ideals , both invariants behave monotonic ... [+]
In this paper we show that the Stanley depth, as well as the usual depth, are essentially determined by the lcm-lattice. More precisely, we show that for quotients of monomial ideals , both invariants behave monotonic with respect to certain maps defined on their lcm-lattice. This allows simple and uniform proofs of many new and known results on the Stanley depth. In particular, we obtain a generalization of our result on polarization presented in [16]. We also obtain a useful description of the class of all monomial ideals with a given lcm-lattice, which is independent from our applications to the Stanley depth. [-]
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Journal of Combinatorial Theory, Series A Volume 150, August 2017Rights
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