The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topologica...

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics s...

This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical inte...

From the reviews of the previous editions".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at ...

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a gl...

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensi...

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 ba...

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact soluti...

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinkingCombinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems.Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geom...

This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and B...

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as ...