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Lectures on Advances in Combinatorics

Rudof Ahlswede and Vladimir Blinovsky
Publisher: 
Springer
Publication Date: 
2008
Number of Pages: 
314
Format: 
Paperback
Series: 
Univesitext
Price: 
59.95
ISBN: 
9783540786016
Category: 
Monograph
[Reviewed by
Miklós Bóna
, on
01/19/2009
]

Two-thirds of the title are correct, and the last third is over-inclusive. Yes, this is a collection of what could perhaps be sixteen lectures at a department colloquium or invited, one-hour addresses at conferences. Yes, all sixteen lectures contain several recent results, which are sometimes only three to five years old. And no, all of combinatorics is of course not covered. A better, more truthful title would have been "Lectures on Advances on Extremal Combinatorics", since the majority of the results discussed in the book can be expressed by an inequality.

The lectures are organized in five independent chapters: Intersection results, Covering and Packing, Dimension-constrained Extremal Problems, Antichain Splittings, and Combinatorial Number theory.

The book has some very useful auxiliary material for researchers, namely the open problems at the end of each chapter, and the Appendix at the end of the book. The latter puts each chapter into context, giving further relevant results and additional open problems. Somewhat unexpectedly for a book of this nature, there are exercises at the end of each chapter as well.

This reviewer does not believe that the book is appropriate for a regular class since the topics are a little bit too specialized and unrelated to each other for that. The writing style is terse. However, the book will be very useful for researchers, and it could serve as the basis of a graduate seminar, where each participant presents the material of one lecture covered in this book.


Miklós Bóna is Associate Professor of Mathematics at the University of Florida.

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