An algorithm for computing the multigraded Hilbert depth of a module. A method for computing the multigraded Hilbert depth of a module was presented in [B. Ichim and J.-J. Moyano-Fernández, Math. Nachr. 287, No. 11–12, 1274–1287 (2014; Zbl 1302.05212)]. 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 [B. Ichim and A. Zarojanu, “Hdepth: An Algorithm for Computing the Multigraded Hilbert Depth of a Module”, Implemented in CoCoA. Available online https://dl.dropboxusercontent.com/s/urhrasy5ntgbwzf/Hdepth.htm]. Thus, we completely solve several open problems proposed in [J. Herzog, Lect. Notes Math. 2083, 3–45 (2013; Zbl 1310.13001)].
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José: How to compute the Stanley depth of a module (2017)
- Duval, Art M.; Goeckner, Bennet; Klivans, Caroline J.; Martin, Jeremy L.: A non-partitionable Cohen-Macaulay simplicial complex (2016)
- Katthän, Lukas: Betti posets and the Stanley depth (2016)
- Ichim, B.; Katthän, L.; Moyano-Fernández, J.J.: The behavior of Stanley depth under polarization (2015)
- Katthän, Lukas: Stanley depth and simplicial spanning trees (2015)
- Popescu, Adrian: An algorithm to compute the Hilbert depth (2015)
- Ichim, Bogdan; Zarojanu, Andrei: An algorithm for computing the multigraded Hilbert depth of a module (2014)
- Popescu, Adrian; Popescu, Dorin: Four generated, squarefree, monomial ideals (2014)