matroids a geometric introduction

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Matroids A Geometric Introduction

Author : Gary Gordon
ISBN : 9781139536080
Genre : Mathematics
File Size : 80. 37 MB
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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.

Matroid Theory

Author : Joseph Edmond Bonin
ISBN : 9780821805084
Genre : Mathematics
File Size : 37. 98 MB
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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.

Matroid Applications

Author : Neil White
ISBN : 0521381657
Genre : Mathematics
File Size : 27. 12 MB
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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).

Matroid Theory

Author : D. J. A. Welsh
ISBN : 9780486474397
Genre : Mathematics
File Size : 65. 16 MB
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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.

Combinatorial Geometries

Author : Neil White
ISBN : 0521333393
Genre : Mathematics
File Size : 82. 7 MB
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This book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists.

Higher Combinatorics

Author : M. Aigner
ISBN : 9789401012201
Genre : Mathematics
File Size : 62. 12 MB
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It is general consensus that Combinatorics has developed into a full-fledged mathematical discipline whose beginnings as a charming pastime have long since been left behind and whose great signifi cance for other branches of both pure and applied mathematics is only beginning to be realized. The last ten years have witnessed a tremendous outburst of activity both in relatively new fields such as Coding Theory and the Theory of Matroids as well as in' more time honored endeavors such as Generating Functions and the Inver sion Calculus. Although the number of text books on these subjects is slowly increasing, there is also a great need for up-to-date surveys of the main lines of research designed to aid the beginner and serve as a reference for the expert. It was the aim of the Advanced Study Institute "Higher Combinatorics" in Berlin, 1976, to help fulfill this need. There were five sections: I. Counting Theory, II. Combinatorial Set Theory and Order Theory, III. Matroids, IV. Designs and V. Groups and Coding Theory, with three principal lecturers in each section. Expanded versions of most lectures form the contents of this book. The Institute was designed to offer, especially to young researchers, a comprehen sive picture of the most interesting developments currently under way. It is hoped that these proceedings will serve the same purpose for a wider audience.

Combinatorial Optimization

Author : Eugene Lawler
ISBN : 9780486143668
Genre : Mathematics
File Size : 84. 83 MB
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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.

Boolean Representations Of Simplicial Complexes And Matroids

Author : John Rhodes
ISBN : 9783319151144
Genre : Mathematics
File Size : 36. 69 MB
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This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.

Matroid Theory

Author : J. G. Oxley
ISBN : 0199202508
Genre : Mathematics
File Size : 73. 22 MB
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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.

Pattern Recognition On Oriented Matroids

Author : Andrey O. Matveev
ISBN : 9783110530841
Genre :
File Size : 80. 72 MB
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