Books on Combinatorics
Combinatorial Theory
Marshall Hall
Wiley-Interscience  July 2, 1998

Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.

Combinatorial Topology
P. S. Alexandrov
Dover Publications  January 29, 1998

Fundamental topological facts, together with detailed explanations of the necessary technical apparatus, constitute this clearly written, well-organized 3-part text. Part 1 deals with certain classic problems without using the formal techniques of homology theory; parts 2 and 3 focus on the central concept of combinatorial topology, the Betti groups. Numerous detailed examples.

Russell Merris
John Wiley & Sons, Inc.  2003

mathematical gem--freshly cleaned and polished

Combinatorics (London Mathematical Society Lecture Note Series)
H. N. V. Temperley
Cambridge University Press  October 30, 1981

Combinatorics Advances
Charles J. Colbourn, Ebdollah Sayed Mahmoodian
Springer  September 30, 1995

The 19 surveys and research papers collected in Combinatorics Advances were presented at the 25th Annual Iranian Conference in Tehran. Keynote papers by Richard Guy and Andreas Dress on combinatorics, combinatorial games, molecular biology and tilings are complemented by invited survey papers on combinatorial design theory and graph theory, and by contributed papers covering graphs, designs, and related combinatorics. The problem session at the conference posed interesting open questions, and these are included in the book. Audience: Informative and stimulating reading for researchers in discrete mathematics at all levels.

Combinatorics and Graph Theory
John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
Springer  October 19, 2005

This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory. Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Pólya theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, K?nig's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic and lively style. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest.

Combinatorics and Partially Ordered Sets
William T. Trotter
The Johns Hopkins University Press  December 18, 2001

Combinatorics and Probability
Graham Brightwell, Imre Leader, Alex Scott, Andrew Thomason
Cambridge University Press  April 2007

Combinatorics is an area of mathematics involving an impressive breadth of ideas, and it encompasses topics ranging from codes and circuit design to algorithmic complexity and algebraic graph theory. In a highly distinguished career Béla Bollobás has made, and continues to make, many significant contributions to combinatorics, and this volume reflects the wide range of topics on which his work has had a major influence. It arises from a conference organized to mark his 60th birthday and the thirty-one articles contained here are of the highest calibre. That so many excellent mathematicians have contributed is testament to the very high regard in which Béla Bollobás is held. Students and researchers across combinatorics and related fields will find that this volume provides a wealth of insight to the state of the art.

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