Mathematics – Combinatorics
Scientific paper
2007-09-22
Mathematics
Combinatorics
79 pages, in German, this is the author's Diplomarbeit (Master's thesis), minor layout improvements
Scientific paper
In dieser Diplomarbeit werden einige Gradschranken f\"ur Erzeugendensysteme und Gr\"obnerbasen 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 Gr\"obnerbasis eines beliebigen (m \times n)-Transportpolytops bez\"uglich einer beliebigen umgekehrt lexikographischen Termordnung hat h\"ochstens Grad mn/2. Wir konstruieren auch ein Beispiel, f\"ur das diese Schranke ann\"ahernd scharf ist. ----- In this Diplomarbeit (Master's thesis), we prove some degree bounds for generating sets and Gr\"obner 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 Gr\"obner 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.
No associations
LandOfFree
Torische Ideale von Flusspolytopen does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Torische Ideale von Flusspolytopen, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Torische Ideale von Flusspolytopen will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-544107