Discrete Mathematics

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two,...

Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to...

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other...

This is a collection of surveys and research papers on topics of interest in combinatorics, given at a conference in Matrahaza, Hungary. Originally published in journal form, it is here reissued as a book due to its special interest. It is dedicated to...

This volume contains survey articles based on the invited lectures given at the Twenty-second British Combinatorial Conference, held in July 2009 at the University of St Andrews. This biennial conference is a well-established international event, with...

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...

Paul Erdoes was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading...

The fifteenth British Combinatorial Conference took place in July 1995 at the University of Stirling. This volume consists of the papers presented by the invited lecturers at the meeting, and provides an up-to-date survey of current research activity in...

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 volume comprises the invited lectures given at the 14th British Combinatorial Conference. The lectures survey many topical areas of current research activity in combinatorics and its applications, and also provide a valuable overview of the subject,...

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...

Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their...

Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, presents a study of...

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...

Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For...

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,...

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...

Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or...

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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 -...