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arXiv · 0709.3570

Torische Ideale von Flusspolytopen

Matthias Lenz
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Abstract

In dieser Diplomarbeit werden einige Gradschranken für Erzeugendensysteme und Gröbnerbasen von torischen Idealen von Flusspolytopen bewiesen. Alle torischen Ideale von Flusspolytopen sind im Grad 3 erzeugt. Glatte (3x4)-Transportpolytope sind sogar im Grad 2 erzeugt. Die reduzierte Gröbnerbasis eines beliebigen (m \times n)-Transportpolytops bezüglich einer beliebigen umgekehrt lexikographischen Termordnung hat höchstens Grad mn/2. Wir konstruieren auch ein Beispiel, für das diese Schranke annähernd scharf ist. ----- In this Diplomarbeit (Master's thesis), we prove some degree bounds for generating sets and Gröbner bases of toric ideals of flow polytopes. All toric ideals of flow polytopes are generated in degree three. Smooth (3x4)-transportation polytopes are even generated in degree 2. The reduced Gröbner basis of an arbitrary (m \times n)-transportation polytope with respect to an arbitrary reverse lexikographic term order has at most degree mn/2. We also construct an example, for which this bound is almost sharp.

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Matthias Lenz. 2007-11-02. Torische Ideale von Flusspolytopen. https://arxiv.org/abs/0709.3570

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