Books on Combinatorics
Design theory
 
Thomas Beth, Dieter Jungnickel, Hanfried Lenz
Cambridge University Press  1999
Description

This is the first volume of a two-volume text on design theory. Since the first edition, there has been extensive development of the theory. In particular, the growing importance of discrete mathematics to many parts of engineering and science has made designs a useful tool for applications. The authors acknowledge this trend with an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering. The book features exercises throughout and concludes with an extensive and updated bibliography of over 1800 entries.

Enumerative Combinatorics
 
Charalambos A. Charalambides
Chapman & Hall/CRC  May 29, 2002
Description

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

Enumerative Combinatorics, Vol. I and Vol. II
 
Richard P. Stanley
Cambridge University Press   April, 1997 and January 5, 1999
Description

Erdos on Graphs
 
Fan R. K. Chung, Paul Erdos and Ronald L. Graham
AK Peters, Ltd.  January 5, 1998
Description

A tribute to Paul Erdos, the wandering mathematician once described as the prince of problem solvers & the absolute monarch of problem posers, examines within the context of his personality & lifestyle the legacy of open problems he left to the world of mathematics after his death in 1996. DLC: Graph theory

Extremal Graph theory
 
Bela Bollobas
Dover Publications  June 4, 2004
Description

The ever-expanding field of extremal graph theory encompasses an array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume presents a concise yet comprehensive treatment, featuring complete proofs for almost all of its results and numerous exercises. 1978 edtion.

Fete of Combinatorics and Computer Science
 
Gyula O.H. Katona, Alexander Schrijver, and Tamás Szönyi
Springer  September 14, 2010
Description

Discrete Mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, whose outstanding scientific work has defined and shaped many research directions in the past 40 years. A number of friends and colleagues, all top authorities in their fields of expertise gathered at the two conferences in August 2008 in Hungary, celebrating Lovász' 60th birthday. It was a real fete of combinatorics and computer science. Some of these plenary speakers submitted their research or survey papers prior to the conferences. These are included in the volume "Building Bridges". The other speakers were able to finish their contribution only later, these are collected in the present volume.

Formal Power Series and Algebraic Combinatorics
 
Dimacs
American Mathematical Society  November, 1995
Description

Foundations of Combinatorics with Applications
 
Edward A. Bender and S. Gill Williamson
Dover Publications  February 6, 2006
Description

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.


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