Exploring core points for fun and profit : A study of lattice-free orbit polytopes

Thomas Rehn

doi:10.18453/rosdok_id00001330

Thomas Rehn

Exploring core points for fun and profit : A study of lattice-free orbit polytopes

Universität Rostock, 2014

https://doi.org/10.18453/rosdok_id00001330

Abstract: This thesis studies minimal lattice-free symmetric polytopes. Lattice-free means that the only integral points in the polytope are its vertices. Symmetric in context of the thesis means that all vertices lie in one single orbit under a group action. The thesis focuses on groups that are permutation groups acting on R^n by permuting coordinates. If a symmetric polytope is lattice-free, its vertices are called core points. Methods to construct core points and applications in symmetric integer linear programming are explored.

doctoral thesis free access

title:

Exploring core points for fun and profit: A study of lattice-free orbit polytopes

contributing persons:

Thomas Rehn[VerfasserIn]
	1049767993
Achill Schürmann , Prof. Dr.[AkademischeR BetreuerIn]
	Universität Rostock, Institut für Mathematik
Marc Pfetsch , Prof. Dr.[AkademischeR BetreuerIn]
	TU Darmstadt, Fachbereich Mathematik

contributing corporate bodies:

Universität Rostock, Mathematisch-Naturwissenschaftliche Fakultät[Grad-verleihende Institution]
	2147083-2

abstract:

This thesis studies minimal lattice-free symmetric polytopes. Lattice-free means that the only integral points in the polytope are its vertices. Symmetric in context of the thesis means that all vertices lie in one single orbit under a group action. The thesis focuses on groups that are permutation groups acting on R^n by permuting coordinates. If a symmetric polytope is lattice-free, its vertices are called core points. Methods to construct core points and applications in symmetric integer linear programming are explored. [English]

Diese Arbeit behandelt gitterpunkt-freie symmetrische Polytope. Gitterpunkt-frei heißt, dass die Ecken des Polytops die einzigen enthaltenen ganzzahligen Punkte sind. Symmetrisch im Kontext dieser Arbeit meint, dass alle Ecken in einem einzigen Orbit einer Gruppenwirkung liegen. Diese Arbeit beschäftigt sich besonders mit Gruppen, die als Permutationsgruppen auf R^n wirken, indem sie Koordinaten permutieren. Die Ecken eines gitterpunkt-freien symmetrischen Polytops werden core points genannt. Es werden Methoden entwickelt, core points zu finden und in ganzzahliger Optimierung anzuwenden. [German]

document type:

doctoral thesis

institution:

Faculty of Mathematics and Natural Sciences

language:

English

subject class (DDC):

510 Mathematics

publication /
production:

Rostock: Universität Rostock

2014

identifiers: