Triangulations Of Oriented Matroids

Author : Francisco Santos
Publisher : American Mathematical Soc.
ISBN 13 : 0821827693
Total Pages : 95 pages
Book Rating : 4.97/5 ( download)

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Download or read book Triangulations of Oriented Matroids written by Francisco Santos and published by American Mathematical Soc.. This book was released on 2002 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Anders Björner
Publisher : Cambridge University Press
ISBN 13 : 052177750X
Total Pages : 564 pages
Book Rating : 4.06/5 ( download)

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Download or read book Oriented Matroids written by Anders Björner and published by Cambridge University Press. This book was released on 1999-11-18 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Author : Achim Bachem
Publisher : Springer Science & Business Media
ISBN 13 : 3642581528
Total Pages : 215 pages
Book Rating : 4.26/5 ( download)

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Download or read book Linear Programming Duality written by Achim Bachem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are intro- duced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start withre- sults on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns of oriented ma- troids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for furt- herreading and the references provide an overview of the research in this field.

Author : Pavel Galashin
Publisher :
ISBN 13 : 9781470475949
Total Pages : 0 pages
Book Rating : 4.44/5 ( download)

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Download or read book Purity and Separation for Oriented Matroids written by Pavel Galashin and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leclerc and Zelevinsky, motivated by the study of quasi-commuting quantum flag minors, introduced the notions of strongly separated and weakly separated collections. These notions are closely related to the theory of cluster algebras, to the combinatorics of the double Bruhat cells, and to the totally positive Grassmannian. A key feature, called the purity phenomenon, is that every maximal by inclusion strongly (resp., weakly) separated collection of subsets in [n] has the same cardinality. In this paper, we extend these notions and define M-separated collections for any oriented matroid M. We show that maximal by size M-separated collections are in bijection with fine zonotopal tilings (if M is a realizable oriented matroid), or with one-element liftings of M in general position (for an arbitrary oriented matroid). We introduce the class of pure oriented matroids for which the purity phenomenon holds: an oriented matroid M is pure if M-separated collections form a pure simplicial complex, i.e., any maximal by inclusion M-separated collection is also maximal by size. We pay closer attention to several special classes of oriented matroids: oriented matroids of rank 3, graphical oriented matroids, and uniform oriented matroids. We classify pure oriented matroids in these cases. An oriented matroid of rank 3 is pure if and only if it is a positroid (up to reorienting and relabeling its ground set). A graphical oriented matroid is pure if and only if its underlying graph is an outerplanar graph, that is, a subgraph of a triangulation of an n-gon. We give a simple conjectural characterization of pure oriented matroids by forbidden minors and prove it for the above classes of matroids (rank 3, graphical, uniform).

Author : Jürgen Bokowski
Publisher : Cambridge University Press
ISBN 13 : 0521849306
Total Pages : 294 pages
Book Rating : 4.02/5 ( download)

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Download or read book Computational Oriented Matroids written by Jürgen Bokowski and published by Cambridge University Press. This book was released on 2006-05-08 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : William R. Pulleyblank
Publisher : Academic Press
ISBN 13 : 148326453X
Total Pages : 387 pages
Book Rating : 4.30/5 ( download)

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Download or read book Progress in Combinatorial Optimization written by William R. Pulleyblank and published by Academic Press. This book was released on 2014-05-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Nobuki Takayama
Publisher : Springer Science & Business Media
ISBN 13 : 3540380841
Total Pages : 467 pages
Book Rating : 4.49/5 ( download)

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Download or read book Mathematical Software - ICMS 2006 written by Nobuki Takayama and published by Springer Science & Business Media. This book was released on 2006-08-24 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.

Author : Rabe v. Randow
Publisher : Springer Science & Business Media
ISBN 13 : 3642516548
Total Pages : 522 pages
Book Rating : 4.42/5 ( download)

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Download or read book Integer Programming and Related Areas written by Rabe v. Randow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of integer programming and combinatorial optimization continue to be areas of great vitality, with an ever increasing number of publications and journals appearing. A classified bibliography thus continues to be necessary and useful today, even more so than it did when the project, of which this is the fifth volume, was started in 1970 in the Institut fur Okonometrie und Operations Research of the University of Bonn. The pioneering first volume was compiled by Claus Kastning during the years 1970 - 1975 and appeared in 1976 as Volume 128 of the series Lecture Notes in Economics and Mathematical Systems published by the Springer Verlag. Work on the project was continued by Dirk Hausmann, Reinhardt Euler, and Rabe von Randow, and resulted in the publication of the second, third, and fourth volumes in 1978, 1982, and 1985 (Volumes 160, 197, and 243 of the above series). The present book constitutes the fifth volume of the bibliography and covers the period from autumn 1984 to the end of 1987. It contains 5864 new publications by 4480 authors and was compiled by Rabe von Randow. Its form is practically identical to that of the first four volumes, some additions having been made to the subject list.

Author :
Publisher :
ISBN 13 : 9814488259
Total Pages : pages
Book Rating : 4.59/5 ( download)

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Download or read book Mathematical Software written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jesus De Loera
Publisher : Springer Science & Business Media
ISBN 13 : 3642129714
Total Pages : 547 pages
Book Rating : 4.11/5 ( download)

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Download or read book Triangulations written by Jesus De Loera and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure behind the algorithms and shows new emerging applications, including hundreds of illustrations, examples, and exercises.