The Theory Of Partitions

Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521637664
Size: 10.33 MB
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Discusses mathematics related to partitions of numbers into sums of positive integers.

Theory Of Matroids

Author: Neil White
Publisher: Cambridge University Press
ISBN: 0521309379
Size: 49.59 MB
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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.

Design Theory

Author: Thomas Beth
Publisher: Cambridge University Press
ISBN: 9780521772310
Size: 38.79 MB
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This is the second edition of the standard text on design theory. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.

Finite Fields

Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521392310
Size: 25.53 MB
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This book is devoted entirely to the theory of finite fields.

Relational Mathematics

Author: Gunther Schmidt
Publisher: Cambridge University Press
ISBN: 0521762685
Size: 53.93 MB
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A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.

Matroid Applications

Author: Neil White
Publisher: Cambridge University Press
ISBN: 9780521381659
Size: 40.23 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).

Nonnegative Matrices And Applications

Author: R. B. Bapat
Publisher: Cambridge University Press
ISBN: 9780521571678
Size: 41.48 MB
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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.

Topics In Structural Graph Theory

Author: Lowell W. Beineke
Publisher: Cambridge University Press
ISBN: 1107244307
Size: 25.34 MB
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The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references.

Algebraic Combinatorics On Words

Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521812207
Size: 63.60 MB
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Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.

Topics In Algebraic Graph Theory

Author: Lowell W. Beineke
Publisher: Cambridge University Press
ISBN: 9780521801973
Size: 75.10 MB
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There is no other book with such a wide scope of both areas of algebraic graph theory.