How to compute the multigraded Hilbert depth of a module

In the first part of this paper we introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module M over the polynomial ring K[X1,...,Xn] by reducing the problem to the computation of the finite set of the new defined Hilbert p...

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Bibliographic Details
Published in:Mathematische Nachrichten 2014-08, Vol.287 (11-12), p.1274-1287
Main Authors: Ichim, Bogdan, Moyano-Fernández, Julio-José
Format: Article
Language:English
Subjects:
05E40
13D40
16W50
Hilbert depth
Hilbert series
partitions
Stanley depth
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Summary:In the first part of this paper we introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module M over the polynomial ring K[X1,...,Xn] by reducing the problem to the computation of the finite set of the new defined Hilbert partitions. In the second part we show how Hilbert partitions may be used for computing the Stanley depth of the module M. In particular, we answer two open questions posed by Herzog in .
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201300120