Books on Combinatorics
Combinatorial design theory
 
Charles J. Colbourn, R. A. Mathon, Alexander Rosa
North-Holland  1987
Description

Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science. This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions. The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.

Combinatorial Designs and Tournaments
 
Combinatorial Designs and Tournaments
Oxford University Press  May 18, 2006
Description

This is an extensively revised version of the very successful ombinatorial Designs: Construction Methods which was published in 1990 by Ellis Horwood and is now out of print. Although the basic material on block designs, difference systems. Latin squares, and Steiner triple systems has been retained, there is greater emphasis on the construction of tournament schedules. A new chapter on league schedules is included, dealing with round robin tournaments, venues sequences, and carry over effects. Balanced tournament designs, double schedules, and bridge tournament designs are also covered, and there is some material on whist tournaments. The presentation is clear and reable. Throughout, the historical development of the material is emphasized. There are plenty of examples and exercises giving detailed constructions, and a copious bibliography is provided. The author is internationally respected as an expositor, and this book provides an excellent student text and reference and book for researchers.

Combinatorial enumeration
 
Ian P. Goulden, David M. Jackson
John Wiley & Sons, Inc.  1983
Description

This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.

Combinatorial Network Theory
 
Ding-Zhu Du, F. Hsu
Springer  September 1, 2006
Description

A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. The book provides a recent solution to this problem. The subject of all five chapters is the interconnection problem. The first two chapters deal with Cayley digraphs which are candidates for networks of maximum connectivity with given degree and number of nodes. Chapter 3 addresses Bruijn digraphs, Kautz digraphs, and their generalizations, which are candidates for networks of minimum diameter and maximum connectivity with given degree and number of nodes. Chapter 4 studies double loop networks, and Chapter 5 considers broadcasting and the Gossiping problem. All the chapters emphasize the combinatorial aspects of network theory. Audience: A vital reference for graduate students and researchers in applied mathematics and theoretical computer science.

Combinatorial Optimization: Algorithm and Complexity
 
Christos H. Papadimitriou, Kenneth Steiglitz
Dover Publications  January 29, 1998
Description

Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. "Mathematicians wishing a self-contained introduction need look no further." — American Mathematical Monthly. 1982 edition.

Combinatorial Optimization: Theory and Algorithms
 
Bernhard Korte, Jens Vygen
Springer  November 10, 2010
Description

Now fully updated in a third edition, this is a comprehensive textbook on combinatorial optimization. It puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete but concise proofs, also for many deep results, some of which have not appeared in print before. Recent topics are covered as well, and numerous references are provided. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.

Combinatorial Problems in Mathematical Competitions
 
Yao Zhang
World Scientific  March 10, 2011
Description

This book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book. With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.

Combinatorial Species and Tree-like Structures
 
F. Bergeron, P. LeRoux, G. Labelle
Cambridge University Press  December 22, 2003
Description

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labeled and unlabeled structures as well as a tool for the specification and analysis of these structures. This key reference presents the basic elements of the theory and gives a unified account of its developments and applications. The authors offer a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya Theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis, and differential equations.


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