Discrete Mathematics

Design theory has grown to be a subject of considerable interest in mathematics, not only in itself, but for its connections to other fields such as geometry, group theory, graph theory and coding theory. This textbook, first published in 1985, is...

This book provides a rapid introduction to topics in graph theory typically covered in a graduate course. The author sets out the main recent results in several areas of current research in graph theory. Topics covered include edge-colourings, symmetries...

This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let...

Originally published in 1996, this is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author's aim is not always to present the most general results, but...

This 2003 book provides an analysis of combinatorial games - games not involving chance or hidden information. It contains a fascinating collection of articles by some well-known names in the field, such as Elwyn Berlekamp and John Conway, plus other...

This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in...

This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the...

The sign-solvability of a linear system implies that the signs of the entries of the solution are determined solely on the basis of the signs of the coefficients of the system. That it might be worthwhile and possible to investigate such linear systems...

This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical...

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix,...

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering,...

Written for a broad audience of students in mathematics, computer science, operations research, statistics, and engineering, this textbook presents a short, lively survey of several fascinating non-calculus topics in modern applied mathematics. Coverage...

Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural...

The British Combinatorial Conference is one of the most well known meetings for combinatorialists. This volume collects the invited talks from the 1999 conference held at the University of Kent and together these span a broad range of combinatorial...

This volume contains the invited lectures given at the Sixteenth British Combinatorial Conference, held in July 1997 at Queen Mary and Westfield College, University of London. This biennial conference is a well-established international event, with...

The study of stable groups connects model theory, algebraic geometry and group theory. It analyses groups which possess a certain very general dependence relation (Shelah's notion of 'forking'), and tries to derive structural properties from this. These...

This volume presents up-to-date research on finite geometries and designs, a key area in modern applicable mathematics. An introductory chapter discusses topics presented in each of the main chapters, and is followed by articles from leading...

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, sometimes they have been considered only as a special class in some wider context. This book deals solely with bipartite...

This book is an introductory text on the combinatorial theory of finite geometry. It assumes only a basic knowledge of set theory and analysis, but soon leads the student to results at the frontiers of research. It begins with an elementary combinatorial...

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive...

Polycycles and symmetric polyhedra appear as generalisations of graphs in the modelling of molecular structures, such as the Nobel prize winning fullerenes, occurring in chemistry and crystallography. The chemistry has inspired and informed many...

The ICMS Workshop on Geometric and Combinatorial Methods in Group Theory, held at Heriot-Watt University in 1993, brought together some of the leading research workers in the subject. Some of the survey articles and contributed papers presented at the...

Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives an account of many of those applications together with a thorough general introduction to both design theory and coding theory -...

Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this book the authors discuss the generalization of results and applications to quasi-symmetric designs. The coverage is comprehensive and will...

This volume contains the invited lectures given at the Twelfth British Combinatorical Conference. The lectures survey the many areas of current research activity in combinatorics and its applications, including graph theory, designs, and probabilistic...

Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. This book presents some of the algebraic techniques that have been brought to...

The articles collected here are the texts of the invited lectures given at the Eighth British Combinatorial Conference held at University College, Swansea. The contributions reflect the scope and breadth of application of combinatorics, and are...

Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe,...

In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational...

Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and...

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,...

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...

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, sometimes they have been considered only as a special class in some wider context. This book deals solely with bipartite...

This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author examines the fundamental developments in the field and...

Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be...

The British Combinatorial Conference is held every two years and is now a key event for mathematicians worldwide, working in combinatorics. This volume is published on the occasion of the 18th meeting, which was held 1st-6th July 2001 at the University...

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal...

Combinatorics is one of the fastest growing ?elds of mathematics. In large measure this is because many practical problems can be modeled and then e?ciently solved using combinatorial theory. This real world motivation for studying algorithmic...

These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs on the one hand, and graph theory on the other. A feature of this book is the...

These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other...