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Circuit Admissible Triangulations Of Oriented Matroids
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Book Synopsis Circuit Admissible Triangulations of Oriented Matroids by : Jörg Rambau
Download or read book Circuit Admissible Triangulations of Oriented Matroids written by Jörg Rambau and published by . This book was released on 2000 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Triangulations of Oriented Matroids by : Francisco Santos
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.
Book Synopsis Oriented Matroids by : Anders Björner
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.
Book Synopsis Computational Oriented Matroids by : Jürgen Bokowski
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.
Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2000 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computing Triangulations Using Oriented Matroids by : Julian Pfeifle
Download or read book Computing Triangulations Using Oriented Matroids written by Julian Pfeifle and published by . This book was released on 2002 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Tropical Oriented Matroids and Triangulations of Products of Simplices by : Kristen Freeman
Download or read book Tropical Oriented Matroids and Triangulations of Products of Simplices written by Kristen Freeman and published by . This book was released on 2009 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Software - ICMS 2006 by : Nobuki Takayama
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.
Download or read book TOPCOM written by Jörg Rambau and published by . This book was released on 2002 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "TOPCOM is a package for computing triangulations of point configurations and oriented matroids. For example, for a point configuration one can compute the chirotope, components of the flip graph of triangulations, enumerate all triangulations. The core algorithms implemented in TOPCOM are described, and implementation issues are discussed."
Book Synopsis Purity and Separation for Oriented Matroids by : Pavel Galashin
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).
Book Synopsis Topology of Oriented Matroids by : Arnaldo Mandel
Download or read book Topology of Oriented Matroids written by Arnaldo Mandel and published by . This book was released on 1982 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oriented Matroids written by and published by . This book was released on 1999 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Mathematics of Chip-Firing by : Caroline J. Klivans
Download or read book The Mathematics of Chip-Firing written by Caroline J. Klivans and published by CRC Press. This book was released on 2018-11-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.
Book Synopsis Supplemento ai Rendiconti del Circolo matematico di Palermo by : Circolo matematico di Palermo
Download or read book Supplemento ai Rendiconti del Circolo matematico di Palermo written by Circolo matematico di Palermo and published by . This book was released on 1994 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Supplemento Ai Rendiconti Del Circolo Matematico Di Palermo by :
Download or read book Supplemento Ai Rendiconti Del Circolo Matematico Di Palermo written by and published by . This book was released on 1994 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence of Unimodular Triangulations–Positive Results by : Christian Haase
Download or read book Existence of Unimodular Triangulations–Positive Results written by Christian Haase and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
