Download or read book Matroids A Geometric Introduction written by Gary Gordon and published by Cambridge University Press. This book was released on 2012-08-02 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.
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.
Download or read book Matrices and Matroids for Systems Analysis written by Kazuo Murota and published by Springer Science & Business Media. This book was released on 1999-11-29 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006
Download or read book Combinatorial Optimization written by Eugene Lawler and published by Courier Corporation. This book was released on 2012-10-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perceptive text examines shortest paths, network flows, bipartite and nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. Suitable for courses in combinatorial computing and concrete computational complexity.
Download or read book Theory of Matroids written by Neil White and published by Cambridge University Press. This book was released on 1986-04-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.
Download or read book Matroid Theory written by Joseph Edmond Bonin and published by American Mathematical Soc.. This book was released on 1996 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory held at the University of Washington, Seattle. The book features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour. Walter Whiteley's article unifies applications of matroid theory to constrained geometrical systems, including the rigidity of bar-and-joint frameworks, parallel drawings, and splines. These widely accessible articles contain many new results and directions for further research and applications. The surveys are complemented by selected short research papers. The volume concludes with a chapter of open problems. Features: Self-contained, accessible surveys of three active research areas in matroid theory. Many new results. Pointers to new research topics. A chapter of open problems. Mathematical applications. Applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.
Download or read book Coxeter Matroids written by Alexandre V. Borovik and published by Springer Science & Business Media. This book was released on 2003-07-11 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
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.
Download or read book Matroid Theory written by D. J. A. Welsh and published by Courier Corporation. This book was released on 2010-01-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.
Download or read book Matroid Theory written by James G. Oxley and published by Oxford University Press, USA. This book was released on 2006 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics. This incisive survey of matroid theory falls into two parts: the first part provides a comprehensive introduction to the basics of matroid theory while the second treats more advanced topics. The book contains over five hundred exercises and includes, for the first time in one place, short proofs for most of the subjects' major theorems. The final chapter lists sixty unsolved problems and details progress towards their solutions.
Download or read book A Source Book in Matroid Theory written by Joseph P. S. Kung and published by . This book was released on 1986 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matroid Applications written by Neil White and published by Cambridge University Press. This book was released on 1992-03-05 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).
Download or read book Matroids A Geometric Introduction written by Gary Gordon and published by Cambridge University Press. This book was released on 2012-08-02 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.
Download or read book Systems Analysis by Graphs and Matroids written by Kazuo Murota and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.
Download or read book Coxeter Matroids written by Alexandre V. Borovik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
Download or read book A Lost Mathematician Takeo Nakasawa written by Hirokazu Nishimura and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matroid theory was invented in the middle of the 1930s by two mathematicians independently, namely, Hassler Whitney in the USA and Takeo Nakasawa in Japan. Whitney became famous, but Nakasawa remained anonymous until two decades ago. He left only four papers to the mathematical community, all of them written in the middle of the 1930s. It was a bad time to have lived in a country that had become as eccentric as possible. Just as Nazism became more and more flamboyant in Europe in the 1930s, Japan became more and more esoteric and fanatical in the same time period. This book explains the little that is known about Nakasawa’s personal life in a Japan that had, among other failures, lost control over its military. This book contains his four papers in German and their English translations as well as some extended commentary on the history of Japan during those years. The book also contains 14 photos of him or his family. Although the veil of mystery surrounding Nakasawa’s life has only been partially lifted, the work presented in this book speaks eloquently of a tragic loss to the mathematical community.
Download or read book Matroid Theory written by László Lovász and published by North Holland. This book was released on 1985 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
