HOW TO COMPUTE THE STANLEY DEPTH OF A MODULE

Autor(en): Ichim, Bogdan
Katthan, Lukas
Jose Moyano-Fernandez, Julio
Stichwörter: ALGORITHM; DECOMPOSITIONS; Graded modules; Hilbert depth; Mathematics; Mathematics, Applied; MULTIGRADED HILBERT DEPTH; Stanley decomposition; Stanley depth
Erscheinungsdatum: 2017
Herausgeber: AMER MATHEMATICAL SOC
Journal: MATHEMATICS OF COMPUTATION
Volumen: 86
Ausgabe: 303
Startseite: 455
Seitenende: 472
Zusammenfassung: 
In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module M over the polynomial ring K[X-1,..., 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 P contains a Z(n)-lattice point.
ISSN: 00255718
DOI: 10.1090/mcom/3106

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