Triangulations of Oriented Matroids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Triangulations of Oriented Matroids write by Francisco Santos. This book was released on 2002. Triangulations of Oriented Matroids available in PDF, EPUB and Kindle. We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Circuit Admissible Triangulations of Oriented Matroids
Circuit Admissible Triangulations of Oriented Matroids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Circuit Admissible Triangulations of Oriented Matroids write by Jörg Rambau. This book was released on 2000. Circuit Admissible Triangulations of Oriented Matroids available in PDF, EPUB and Kindle. Abstract: "All triangulations of euclidean oriented matroids are of the same PL-homeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PL-spheres. For non-euclidean oriented matroids this question is wide open. One key point in the proof of Anderson is the following fact: for every triangulation of a euclidean oriented matroid the adjacency graph of the set of all simplices 'intersecting' a segment [p-p+] is a path. We call this graph the [p-p+]-adjacency graph of the triangulation. While we cannot solve the problem of the topological type of triangulations of general oriented matroids we show in this note that for every circuit admissible triangulation of an arbitrary oriented matroid the [p-p+] adjacency graph is path."
Computing Triangulations Using Oriented Matroids
Computing Triangulations Using Oriented Matroids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computing Triangulations Using Oriented Matroids write by Julian Pfeifle. This book was released on 2002. Computing Triangulations Using Oriented Matroids available in PDF, EPUB and Kindle. Abstract: "Oriented matroids are combinatorial structures that encode the combinatorics of point configurations. The set of all triangulations of a point configuration depends only on its oriented matroid. We survey the most important ingredients necessary to exploit oriented matroids as a data structure for computing all triangulations of a point configuration, and report on experience with an implementation of these concepts in the software package TOPCOM. Next, we briefly overview the construction and an application of the secondary polytope of a point configuration, and calculate some examples illustrating how our tools were integrated into the POLYMAKE framework."
Oriented Matroids
Oriented Matroids - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Oriented Matroids write by Anders Björner. This book was released on 1999-11-18. Oriented Matroids available in PDF, EPUB and Kindle. First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.
Tropical Oriented Matroids and Triangulations of Products of Simplices
Tropical Oriented Matroids and Triangulations of Products of Simplices - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tropical Oriented Matroids and Triangulations of Products of Simplices write by Kristen Freeman. This book was released on 2009. Tropical Oriented Matroids and Triangulations of Products of Simplices available in PDF, EPUB and Kindle.
