An Algorithm for Computing the Multigraded Hilbert Depth of a Module

Abstract

A method for computing the multigraded Hilbert depth of a module was presented in [Ichim and Moyano-Fernández 14]. In this paper, we improve the method and we introduce an effective algorithm for performing the computations. In a particular case, the algorithm may also be easily adapted for computing the Stanley depth of the module. We further present interesting examples that were found with the help of an experimental implementation of the algorithm Hdepth [Ichim and Zarojanu 13]. Thus, we completely solve several open problems proposed in [Herzog 13].

2000 AMS Subject Classification::

• Primary: 05E40
• Secondary: 68R05

Keywords::

• Hilbert depth
• Stanley depth
• computational experiments

Notes

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