Theory Of Matroids

Author : Neil White
Publisher : Cambridge University Press
Page : 341 pages
File Size : 42,6 Mb
Release : 1986-04-03
Category : Mathematics
ISBN : 9780521309370

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Theory of Matroids by Neil White Pdf

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.

Author : D. J. A. Welsh
Publisher : Courier Corporation
Page : 450 pages
File Size : 52,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486474397

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Matroid Theory by D. J. A. Welsh Pdf

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.

Author : Gary Gordon,Jennifer McNulty
Publisher : Cambridge University Press
Page : 411 pages
File Size : 55,8 Mb
Release : 2012-08-02
Category : Language Arts & Disciplines
ISBN : 9780521145688

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Matroids: A Geometric Introduction by Gary Gordon,Jennifer McNulty Pdf

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Author : Joseph Edmond Bonin
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 41,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805084

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Matroid Theory by Joseph Edmond Bonin Pdf

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; and applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.

Author : Kazuo Murota
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 51,6 Mb
Release : 1999-11-29
Category : Mathematics
ISBN : 3540660240

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Matrices and Matroids for Systems Analysis by Kazuo Murota Pdf

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

Author : Anders Björner
Publisher : Cambridge University Press
Page : 564 pages
File Size : 51,7 Mb
Release : 1999-11-18
Category : Mathematics
ISBN : 9780521777506

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Oriented Matroids by Anders Björner Pdf

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Author : László Lovász,András Recski
Publisher : North Holland
Page : 448 pages
File Size : 49,6 Mb
Release : 1985
Category : Science
ISBN : UOM:39015037748509

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Matroid Theory by László Lovász,András Recski Pdf

Author : Andras Recski
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 49,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662221433

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Matroid Theory and its Applications in Electric Network Theory and in Statics by Andras Recski Pdf

I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen eral tools that can be learned and then applied, to various problems. Matroid theory is one of these tools. (2) Within combinatorics, the relative importance of algorithms has in creased with the spread of computers. Classical analysis did not even consider problems where "only" a finite number of cases were to be studied. Now such problems are not only considered, but their complexity is often analyzed in con siderable detail. Some questions of this type (for example, the determination of when the so called "greedy" algorithm is optimal) cannot even be answered without matroidal tools.

Author : Joseph P. S. Kung
Publisher : Unknown
Page : 424 pages
File Size : 42,9 Mb
Release : 1986
Category : Matroids
ISBN : UCSD:31822002756054

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A Source Book in Matroid Theory by Joseph P. S. Kung Pdf

Author : Leonidas S. Pitsoulis
Publisher : Springer Science & Business Media
Page : 127 pages
File Size : 53,9 Mb
Release : 2013-10-24
Category : Mathematics
ISBN : 9781461489573

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Topics in Matroid Theory by Leonidas S. Pitsoulis Pdf

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

Author : Neil White
Publisher : Cambridge University Press
Page : 377 pages
File Size : 43,7 Mb
Release : 1992-03-05
Category : Mathematics
ISBN : 9780521381659

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Matroid Applications by Neil White Pdf

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).

Author : Jürgen Bokowski
Publisher : Cambridge University Press
Page : 294 pages
File Size : 49,5 Mb
Release : 2006-05-08
Category : Computers
ISBN : 9780521849302

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Computational Oriented Matroids by Jürgen Bokowski Pdf

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 : W. T. Tutte
Publisher : Unknown
Page : 84 pages
File Size : 49,7 Mb
Release : 1971
Category : Matroids
ISBN : 0044400969

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Introduction to the Theory of Matroids by W. T. Tutte Pdf

Author : Kazuo Murota
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615863

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Systems Analysis by Graphs and Matroids by Kazuo Murota Pdf

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.

Author : Koh Khee Meng,Dong Fengming,Tay Eng Guan
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 48,9 Mb
Release : 2007-03-15
Category : Mathematics
ISBN : 9789813101630

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Introduction to Graph Theory by Koh Khee Meng,Dong Fengming,Tay Eng Guan Pdf

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.