Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

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### Matroid Applications

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).

### Matroids: A Geometric Introduction

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

### Topics in Matroid Theory

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.

### Handbook of Combinatorics

Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.

### Matroid Theory and Its Applications

Lectures: T.H. Brylawski: The Tutte polynomial.- D.J.A. Welsh: Matroids and combinatorial optimisation.- Seminars: M. Barnabei, A. Brini, G.-C. Rota: Un’introduzione alla teoria delle funzioni di Möbius.- A. Brini: Some remarks on the critical problem.- J. Oxley: On 3-connected matroids and graphs.- R. Peele: The poset of subpartitions and Cayley’s formula for the complexity of a complete graph.- A. Recski: Engineering applications of matroids.- T. Zaslavisky: Voltage-graphic matroids.

### Matroid Theory

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 new in paperback version of the classic "Matroid Theory" by James Oxley provides a comprehensive introduction to matroid theory, covering the very basics to more advanced topics. With over 500 exercisesand proofs of major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science. The final chapter lists sixty unsolved problems and describes progress towards their solutions.

### Matroid Theory

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.

### Graphs on Surfaces

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

### Integer Programming and Combinatorial Optimization

The optimistic predictions of a number of microbiologists notwithstanding, the past decade has not signaled the end of infectious disease, but rather an introduction to a host of new and complex microorganisms and their resulting depredations on humanity. The identification of new pathogens, such as the causative agent of Lyme disease and the Human Immuno-deficiency Virus (HIV), as well as the Hepatitis Delta Virus (HDV) has not only revealed new forms of clinical pathology, but new and unexpected variations on the life cycle and the molecular biology of the pathogens. In this volume a number of the leaders in the field of Hepatitis Delta virus research, ranging from clinicians and virologists to molecular biologists and biochemists describe what in their experience typifies some of these unique features.

### Local systems on the complexification of an oriented matroid

### Matroid Theory

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.

### Oriented Matroids

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

### Combinatorial Optimization

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This fifth edition has again been updated, revised, and significantly extended, with more than 60 new exercises and new material on various topics, including Cayley's formula, blocking flows, faster b-matching separation, multidimensional knapsack, multicommodity max-flow min-cut ratio, and sparsest cut. Thus, this book represents the state of the art of combinatorial optimization.

### Workshop on large scale networks & systems

### Matching Theory

This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics. The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in 1986, by launching (among other things) the Markov Chain Monte Carlo method.

### Finite Fields and Applications

This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.

### Journal of combinatorial theory

### Graph Theory with Applications

Salient Features * Over 1500 Problems Are Used To Illustrate Concepts, Related To Different Topics, And Introduce Applications. * Over 1000 Exercises In The Text With Many Different Types Of Questions Posed. * Precise Mathematical Language Is Used Without Excessive Formalism And Abstraction. * Care Has Been Taken To Balance The Mix Of Notation And Words In Mathematical Statements. * Problem Sets Are Stated Clearly And Unambiguously, And All Are Carefully Graded For Various Levels Of Difficulty. * This Text Has Been Carefully Designed For Flexible Use.

### Computational Oriented Matroids

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.

### Bulletin (new Series) of the American Mathematical Society

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Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 8319

Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 0521145686

Category: Language Arts & Disciplines

Page: 393

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Author: Leonidas S. Pitsoulis

Publisher: Springer Science & Business Media

ISBN: 1461489571

Category: Mathematics

Page: 127

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Author: Ronald L. Graham,Martin Grötschel,László Lovász

Publisher: Elsevier

ISBN: 9780444823465

Category: Mathematics

Page: 2198

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*Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), Italy, August 24 - September 2, 1980*

Author: A. Barlotti

Publisher: Springer Science & Business Media

ISBN: 9783642111105

Category: Mathematics

Page: 424

View: 1248

Author: J. G. Oxley

Publisher: Oxford University Press, USA

ISBN: 9780199202508

Category: Mathematics

Page: 532

View: 5499

*AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory, July 2-6, 1995, University of Washington, Seattle*

Author: Joseph Edmond Bonin

Publisher: American Mathematical Soc.

ISBN: 0821805088

Category: Mathematics

Page: 418

View: 1751

*Dualities, Polynomials, and Knots*

Author: Joanna A. Ellis-Monaghan,Iain Moffatt

Publisher: Springer Science & Business Media

ISBN: 1461469716

Category: Mathematics

Page: 139

View: 9385

*4th International IPCO Conference, Copenhagen, Denmark, May 29 - 31, 1995. Proceedings*

Author: Egon Balas,Jens Clausen

Publisher: Springer Science & Business Media

ISBN: 9783540594086

Category: Business & Economics

Page: 461

View: 8562

Author: Graham C. Denham

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

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Author: D. J. A. Welsh

Publisher: Courier Corporation

ISBN: 0486474399

Category: Mathematics

Page: 433

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Author: Anders Björner

Publisher: Cambridge University Press

ISBN: 9780521777506

Category: Mathematics

Page: 548

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*Theory and Algorithms*

Author: Bernhard Korte,Jens Vygen

Publisher: Springer Science & Business Media

ISBN: 3642244882

Category: Mathematics

Page: 660

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Author: Institute of Electrical and Electronics Engineers

Publisher: N.A

ISBN: N.A

Category: Technology & Engineering

Page: 48

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Author: László Lovász,M. D. Plummer

Publisher: American Mathematical Soc.

ISBN: 0821847597

Category: Mathematics

Page: 547

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*7th International Conference, Fq7, Toulouse, France, May 5-9, 2003, Revised Papers*

Author: Gary L. Mullen,Alain Poli

Publisher: Springer Science & Business Media

ISBN: 3540213244

Category: Computers

Page: 261

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Author: N.A

Publisher: N.A

ISBN: N.A

Category:

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Author: C. Vasudev

Publisher: New Age International

ISBN: 812241737X

Category: Graph theory

Page: 466

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*Equivalence Classes of Matrices Within a Natural Framework*

Author: Jürgen Bokowski

Publisher: Cambridge University Press

ISBN: 0521849306

Category: Computers

Page: 323

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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