Triangulations Of Oriented Matroids
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Triangulations Of Oriented Matroids
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Author : Francisco Santos
language : en
Publisher:
Release Date : 2014-09-11
Triangulations Of Oriented Matroids written by Francisco Santos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Oriented matroids categories.
The author considers the concept of triangulation of an oriented matroid. He provides 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 the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M} DEGREES*$, via the so-called lifting triangulations is studied, showing 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 pol
Triangulations Of Oriented Matroids
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Author : Francisco Santos
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Triangulations Of Oriented Matroids written by Francisco Santos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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
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Author : Jörg Rambau
language : en
Publisher:
Release Date : 2000
Circuit Admissible Triangulations Of Oriented Matroids written by Jörg Rambau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Matroids categories.
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."
Oriented Matroids
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Author : Anders Björner
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18
Oriented Matroids written by Anders Björner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.
Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was first published.
Computational Oriented Matroids
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Author : Jürgen Bokowski
language : en
Publisher: Cambridge University Press
Release Date : 2006-05-08
Computational Oriented Matroids written by Jürgen Bokowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-08 with Computers categories.
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
Handbook Of Discrete And Computational Geometry
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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Handbook Of Discrete And Computational Geometry Second Edition
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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2004-04-13
Handbook Of Discrete And Computational Geometry Second Edition written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-13 with Mathematics categories.
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies
Progress In Combinatorial Optimization
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Author : William R. Pulleyblank
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Progress In Combinatorial Optimization written by William R. Pulleyblank and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Mathematical Software Proceedings Of The First International Congress Of Mathematical Software
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Author : Arjeh M Cohen
language : en
Publisher: World Scientific
Release Date : 2002-07-26
Mathematical Software Proceedings Of The First International Congress Of Mathematical Software written by Arjeh M Cohen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-26 with Mathematics categories.
The advent of mathematical software has been one of the most important events in mathematics. Mathematical software systems are used to construct examples, to prove theorems, and to find new mathematical phenomena. On the other hand, mathematical research often motivates developments of new algorithms and new systems.This volume contains the papers presented at the First International Congress of Mathematical Software, which aimed at a coherent study of mathematical software systems from a wide variety of branches of mathematics. The book discusses more than one hundred mathematical software systems. Readers can get an overview of the current status of the arts of mathematical software and algorithms.The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)