How to compute the Stanley depth of a module

Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José

doi:10.1090/mcom/3106

How to compute the Stanley depth of a module
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by Bogdan Ichim, Lukas Katthän and Julio José Moyano-Fernández PDF

Math. Comp. 86 (2017), 455-472 Request permission

Abstract:

In this paper we introduce an algorithm for computing the Stanley depth of a finitely generated multigraded module $M$ over the polynomial ring $\mathbb {K}[X_1, \ldots , X_n]$. 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 $\mathscr {P}$ contains a $\mathbb {Z}^n$-lattice point.

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