Matroids: A Geometric Introduction

Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 0521145686

Category: Language Arts & Disciplines

Page: 393

View: 6018

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

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 2205

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).

Semimodular Lattices

Author: N.A

Publisher: Springer-Verlag

ISBN: 3663124789

Category: Technology & Engineering

Page: 237

View: 354

Theory of Matroids

Author: Neil White

Publisher: Cambridge University Press

ISBN: 0521309379

Category: Mathematics

Page: 316

View: 5212

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.

Topics in Matroid Theory

Author: Leonidas S. Pitsoulis

Publisher: Springer Science & Business Media

ISBN: 1461489571

Category: Mathematics

Page: 127

View: 7230

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.

Matroide

eine Einführung für Mathematiker und Informatiker

Author: Peter Läuchli

Publisher: vdf Hochschulverlag AG

ISBN: 9783728124708

Category:

Page: 136

View: 380

Handbook of Incidence Geometry

Buildings and Foundations

Author: Francis Buekenhout

Publisher: North-Holland

ISBN: 9780444883551

Category: Mathematics

Page: 1420

View: 4691

This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively. More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.

The Theory of Partitions

Author: George E. Andrews

Publisher: Cambridge University Press

ISBN: 9780521637664

Category: Mathematics

Page: 255

View: 5416

Discusses mathematics related to partitions of numbers into sums of positive integers.

Revue de mathématique élémentaires

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5582

Elemente der Mathematik (EL) publishes survey articles about important developments in the field of mathematics; stimulating shorter communications that tackle more specialized questions; and papers that report on the latest advances in mathematics and applications in other disciplines. The journal does not focus on basic research. Rather, its articles seek to convey to a wide circle of readers - teachers, students, engineers, professionals in industry and administration - the relevance, intellectual challenge and vitality of mathematics today. The Problems Section, covering a diverse range of exercises of varying degrees of difficulty, encourages an active grappling with mathematical problems.

Oriented Matroids

Author: Anders Björner

Publisher: Cambridge University Press

ISBN: 9780521777506

Category: Mathematics

Page: 548

View: 9156

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

Combinatorial Geometries

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

View: 7227

This book is a continuation of Theory of Matroids and again consists of a series of related surveys.

Graphs on Surfaces

Dualities, Polynomials, and Knots

Author: Joanna A. Ellis-Monaghan,Iain Moffatt

Publisher: Springer Science & Business Media

ISBN: 1461469716

Category: Mathematics

Page: 139

View: 5985

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.

Bulletin

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3365

Algebra

Author: Paul Moritz Cohn

Publisher: John Wiley & Sons Inc

ISBN: 9780471928409

Category: Mathematics

Page: 486

View: 8946

Semimodular Lattices

Theory and Applications

Author: Manfred Stern

Publisher: Cambridge University Press

ISBN: 9780521461054

Category: Mathematics

Page: 370

View: 1105

A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.

Nonnegative Matrices and Applications

Author: R. B. Bapat,T. E. S. Raghavan

Publisher: Cambridge University Press

ISBN: 9780521571678

Category: Mathematics

Page: 336

View: 5372

This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.