Stanley depth and the lcm-lattice

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:150

Article

Ichim, Bogdan¹  Katthan, Lukas²  Jose Moyano-Fernandez, Julio^3,4 

[1] Romanian Acad, Simion Stoilow Inst Math, Res Unit 5,CP 1-764, Bucharest 014700, Romania

[2] Goethe Univ Frankfurt, FB Informat & Math, D-60054 Frankfurt, Germany

[3] Univ Jaume 1, Dept Matemat, Campus Riu Sec, Castellon De La Plana 12071, Spain

[4] Univ Jaume 1, Inst Univ Matemat & Aplicac Castello, Campus Riu Sec, Castellon De La Plana 12071, Spain

关键词: Monomial ideal;    lcm-lattice;    Stanley depth;    Stanley decomposition;   

DOI  :  10.1016/j.jcta.2017.03.005

来源: Elsevier

【 摘 要 】

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 I/J of monomial ideals J subset of I, 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free