How to compute the Stanley depth of a module

In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module M over the polynomial ring \mathbb{K}[X_1, \ldots , X_n]. As an application, we give an example of a module whose Stanley depth is strictly greater than the depth of its syzygy module....

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Bibliographic Details
Published in:Mathematics of computation 2017-01, Vol.86 (303), p.455-472
Main Authors: ICHIM, BOGDAN, KATTHÄN, LUKAS, MOYANO-FERNÁNDEZ, JULIO JOSÉ
Format: Article
Language:English
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Summary:In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module M over the polynomial ring \mathbb{K}[X_1, \ldots , X_n]. As an application, we give an example of a module whose Stanley depth is strictly greater than the depth of its syzygy module. In particular, we obtain complete answers for two open questions raised by Herzog. Moreover, we show that the question whether M has Stanley depth at least r can be reduced to the question whether a certain combinatorially defined polytope \mathscr {P} contains a \mathbb{Z}^n-lattice point.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3106