How to compute the multigraded Hilbert depth of a module

Abstract

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[X-1,..., X-n] 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 [8]. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim