Topics In Matroid Theory

Author : Leonidas S. Pitsoulis
Publisher : Springer Science & Business Media
Page : 127 pages
File Size : 49,5 Mb
Release : 2013-10-24
Category : Mathematics
ISBN : 9781461489573

Get Book

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 : D. J. A. Welsh
Publisher : Courier Corporation
Page : 450 pages
File Size : 42,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486474397

Get Book

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 : Joseph Edmond Bonin
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 47,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805084

Get Book

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 : Gary Gordon,Jennifer McNulty
Publisher : Cambridge University Press
Page : 411 pages
File Size : 53,8 Mb
Release : 2012-08-02
Category : Language Arts & Disciplines
ISBN : 9780521145688

Get Book

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 : Andras Recski
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 45,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662221433

Get Book

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 : Neil White
Publisher : Cambridge University Press
Page : 341 pages
File Size : 48,9 Mb
Release : 1986-04-03
Category : Mathematics
ISBN : 9780521309370

Get Book

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 : Joseph P. S. Kung
Publisher : Unknown
Page : 424 pages
File Size : 40,8 Mb
Release : 1986
Category : Matroids
ISBN : UCSD:31822002756054

Get Book

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

Author : KUNG
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 43,6 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781468491999

Get Book

A Source Book in Matroid Theory by KUNG Pdf

by Gian-Carlo Rota The subjects of mathematics, like the subjects of mankind, have finite lifespans, which the historian will record as he freezes history at one instant of time. There are the old subjects, loaded with distinctions and honors. As their problems are solved away and the applications reaped by engineers and other moneymen, ponderous treatises gather dust in library basements, awaiting the day when a generation as yet unborn will rediscover the lost paradise in awe. Then there are the middle-aged subjects. You can tell which they are by roaming the halls of Ivy League universities or the Institute for Advanced Studies. Their high priests haughtily refuse fabulous offers from eager provin cial universities while receiving special permission from the President of France to lecture in English at the College de France. Little do they know that the load of technicalities is already critical, about to crack and submerge their theorems in the dust of oblivion that once enveloped the dinosaurs. Finally, there are the young subjects-combinatorics, for instance. Wild eyed individuals gingerly pick from a mountain of intractable problems, chil dishly babbling the first words of what will soon be a new language. Child hood will end with the first Seminaire Bourbaki. It could be impossible to find a more fitting example than matroid theory of a subject now in its infancy. The telltale signs, for an unfailing diagnosis, are the abundance of deep theorems, going together with a paucity of theories.

Author : Neil White
Publisher : Unknown
Page : 338 pages
File Size : 49,9 Mb
Release : 2008
Category : Matroids
ISBN : 1139886169

Get Book

Theory of Matroids by Neil White Pdf

Author : Kazuo Murota
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 44,8 Mb
Release : 1999-11-29
Category : Mathematics
ISBN : 3540660240

Get Book

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 : Neil White
Publisher : Cambridge University Press
Page : 377 pages
File Size : 41,6 Mb
Release : 1992-03-05
Category : Mathematics
ISBN : 9780521381659

Get Book

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 : Alexandre V. Borovik,Israel M. Gelfand,Neil White
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220664

Get Book

Coxeter Matroids by Alexandre V. Borovik,Israel M. Gelfand,Neil White Pdf

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.

Author : James G. Oxley
Publisher : Oxford University Press, USA
Page : 550 pages
File Size : 52,5 Mb
Release : 2006
Category : Mathematics
ISBN : 0199202508

Get Book

Matroid Theory by James G. Oxley Pdf

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.

Author : Neil White
Publisher : Unknown
Page : 376 pages
File Size : 45,8 Mb
Release : 1992
Category : Electronic books
ISBN : 1107094267

Get Book

Matroid Applications by Neil White Pdf

This volume deals with the applications of matroid theory to a variety of topics.

Author : J. E. Graver,M. E. Watkins
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299141

Get Book

Combinatorics with Emphasis on the Theory of Graphs by J. E. Graver,M. E. Watkins Pdf

Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of unformulated or unrecognized general theorems. The body of knowledge has now reached a stage where approaches toward unification are overdue. To paraphrase Professor Gian-Carlo Rota (Toronto, 1967), "Combinatorics needs fewer theorems and more theory. " In this book we are doing two things at the same time: A. We are presenting a unified treatment of much of combinatorics and graph theory. We have constructed a concise algebraically based, but otherwise self-contained theory, which at one time embraces the basic theorems that one normally wishes to prove while giving a common terminology and framework for the develop ment of further more specialized results. B. We are writing a textbook whereby a student of mathematics or a mathematician with another specialty can learn combinatorics and graph theory. We want this learning to be done in a much more unified way than has generally been possible from the existing literature. Our most difficult problem in the course of writing this book has been to keep A and B in balance. On the one hand, this book would be useless as a textbook if certain intuitively appealing, classical combinatorial results were either overlooked or were treated only at a level of abstraction rendering them beyond all recognition.