Mathematics

Theory of Matroids

Author: Neil White

Publisher: Cambridge University Press

ISBN: 0521309379

Category: Mathematics

Page: 316

View: 8117

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.
Mathematics

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 6578

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).
Mathematics

Oriented Matroids

Author: Anders Björner

Publisher: Cambridge University Press

ISBN: 9780521777506

Category: Mathematics

Page: 548

View: 4963

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

The Theory of Partitions

Author: George E. Andrews

Publisher: Cambridge University Press

ISBN: 9780521637664

Category: Mathematics

Page: 255

View: 4280

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

Semimodular Lattices

Theory and Applications

Author: Manfred Stern

Publisher: Cambridge University Press

ISBN: 9780521461054

Category: Mathematics

Page: 370

View: 2158

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

Relational Mathematics

Author: Gunther Schmidt

Publisher: Cambridge University Press

ISBN: 0521762685

Category: Computers

Page: 567

View: 7654

A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.
Mathematics

Permanents

Author: Henryk Minc

Publisher: Cambridge University Press

ISBN: 9780521302265

Category: Mathematics

Page: 224

View: 5075

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.
Language Arts & Disciplines

Matroids: A Geometric Introduction

Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 0521145686

Category: Language Arts & Disciplines

Page: 393

View: 1757

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

Graph Theory Applications

Author: L.R. Foulds

Publisher: Springer Science & Business Media

ISBN: 9780387975993

Category: Mathematics

Page: 385

View: 2815

This text offers an introduction to the theory of graphs and its application in engineering and science. The first part covers the main graph theoretic topics and in the second part, these concepts are applied to problems in engineering, operations reserach, and science. Written at an advanced undergraduate to beginning graduate level, the book is suitable for students of mathematics, engineering, operations resrach, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling.
Mathematics

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 6021

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).
Mathematics

Model Theory

Author: Wilfrid Hodges

Publisher: Cambridge University Press

ISBN: 9780521304429

Category: Mathematics

Page: 772

View: 6652

Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
Mathematics

Topics in Matroid Theory

Author: Leonidas S. Pitsoulis

Publisher: Springer Science & Business Media

ISBN: 1461489571

Category: Mathematics

Page: 127

View: 2388

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.
Mathematics

Combinatorial Species and Tree-like Structures

Author: François Bergeron,Gilbert Labelle,Pierre Leroux

Publisher: Cambridge University Press

ISBN: 9780521573238

Category: Mathematics

Page: 457

View: 3607

Provides a unified understanding of the use of generating functions for labelled and unlabelled structures.
Mathematics

Combinatorial Matrix Theory

Author: Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović

Publisher: Birkhäuser

ISBN: 3319709534

Category: Mathematics

Page: 219

View: 5723

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.
Mathematics

Combinatorial Geometries

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

View: 6273

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.
Mathematics

Matroid Theory

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: 974

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.
Mathematics

Handbook of Incidence Geometry

Buildings and Foundations

Author: Francis Buekenhout

Publisher: North-Holland

ISBN: 9780444883551

Category: Mathematics

Page: 1420

View: 5560

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.
Mathematics

Congressus Numerantium

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2752