Theory of Matroids

Author: Neil White
Publisher: Cambridge University Press
ISBN: 0521309379
Format: PDF, ePub, Mobi
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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.

Matroid Applications

Author: Neil White
Publisher: Cambridge University Press
ISBN: 9780521381659
Format: PDF, Mobi
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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).

Oriented Matroids

Author: Anders Björner
Publisher: Cambridge University Press
ISBN: 9780521777506
Format: PDF, ePub
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First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

The Theory of Partitions

Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521637664
Format: PDF, ePub
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Discusses mathematics related to partitions of numbers into sums of positive integers.

Semimodular Lattices

Author: Manfred Stern
Publisher: Cambridge University Press
ISBN: 9780521461054
Format: PDF, Kindle
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A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.

Permanents

Author: Henryk Minc
Publisher: Cambridge University Press
ISBN: 9780521302265
Format: PDF, ePub, Docs
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The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Relational Mathematics

Author: Gunther Schmidt
Publisher: Cambridge University Press
ISBN: 0521762685
Format: PDF, Mobi
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A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.

Matroid Theory

Author: Joseph Edmond Bonin
Publisher: American Mathematical Soc.
ISBN: 0821805088
Format: PDF, Mobi
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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.

Combinatorial Geometries

Author: Neil White
Publisher: Cambridge University Press
ISBN: 9780521333399
Format: PDF, Mobi
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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.

Matroids A Geometric Introduction

Author: Gary Gordon
Publisher: Cambridge University Press
ISBN: 1139536087
Format: PDF, Mobi
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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.