Extremal Combinatorics

The author is a professor at the Goethe Universität Frankfurt and he is also a member of the Vilnius University Institute of Mathematics and Informatics. His main fields of research are theoretical computer science and discrete mathematics, in particular complexity.

• Preface.- Prolog: What this Book Is About.- Notation.- Counting.- Advanced Counting.- Probabilistic Counting.- The Pigeonhole Principle.- Systems of Distinct Representatives.- Sunflowers.- Intersecting Families.- Chains and Antichains.- Blocking Sets and the Duality.- Density and Universality.- Witness Sets and Isolation.- Designs.- The Basic Method.- Orthogonality and Rank Arguments.- Eigenvalues and Graph Expansion.- The Polynomial Method.- Combinatorics of Codes.- Linearity of Expectation.- The Lovász Sieve.- The Deletion Method.- The Second Moment Method.- The Entropy Function.- Random Walks.- Derandomization.- Ramseyan Theorems for Numbers.- The Hales–Jewett Theorem.- Applications in Communications Complexity.- References.- Index.

From the reviews of the second edition: "This is an entertaining and impressive book. I say impressive because the author managed to cover a very large part of combinatorics in 27 short chapters, without assuming any graduate-level knowledge of the material. ... The collection of topics covered is another big advantage of the book. ... The book is ideal as reference material or for a reading course for a dedicated graduate student. One could teach a very enjoyable class from it as well ... ." (Miklos Bona, The Mathematical Association of America, May, 2012) "[R]eaders interested in any branch of combinatorics will find this book compelling. ... This book is very suitable for advanced undergraduate and graduate mathematics and computer science majors. It requires a very solid grounding in intermediate-level combinatorics and an appreciation for several proof methods, but it is well worth the study." (G.M. White, ACM Computing Reviews, May 2012) "This is the second edition of a well-received textbook. It has been extended with new and updated results. Typographical errors in the first edition are corrected. ... This textbook is suitable for advanced undergraduate or graduate students as well as researchers working in discrete mathematics or theoretical computer science. The author's enthusiasm for the subject is evident and his writing is clear and smooth. This is a book deserving recommendation." (Ko-Wei Lih, Zentralblatt MATH, Vol. 1239, 2012) "This is an introductory book that deals with the subject of extremal combinatorics. ... The book is nicely written and the author has included many elegant and beautiful proofs. The book contains many interesting exercises that will stimulate the motivated reader to get a better understanding of this area. ... author's goal of writing a self-contained book that is more or less up to date ... and that is accessible to graduate and motivated undergraduate students in mathematics and computer science, has been successfully achieved." (Sebastian M. Cioaba, Mathematical Reviews, January, 2013)