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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geprüft am 04.06.2024