Overview
- Provides an introductory, self-contained and up-to-date source in extremal combinatorics suitable for a broad community: mathematicians, computer scientists, and engineers
- Covers a substantial part of the field of combinatorics
- Presents unexpected connections between classical combinatorics, probability and linear algebra
- Proofs are extremely elegant and given in full details
- Includes supplementary material: sn.pub/extras
Part of the book series: Texts in Theoretical Computer Science. An EATCS Series (TTCS)
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Table of contents (32 chapters)
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The Linear Algebra Method
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The Probabilistic Method
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Fragments of Ramsey Theory
Keywords
About this book
Reviews
From the reviews:
"This monograph deals with problems of the following type: ‘If a collection of finite objects … satisfies certain restrictions, how large or how small can it be?’ The text is self-contained and assumes no special knowledge (only a standard mathematical background). Moreover, its 29 chapters – ‘each devoted to a particular proof technique’ – are (almost) independent. Because of this modularity, its style … and the character of its subject, this book can also be browsed and read for (mathematical) pleasure." (P. Schmitt, Monatshefte für Mathematik, Vol. 141 (1), 2004)
"The book is structured as a collection of short, largely independent chapters, each dedicated to a specific proof technique. … The book is broad in scope and gives equal space to the classical counting techniques and to more recent methods. … I used the book to teach a small group of graduate students. It was a rewarding experience. … The material was interesting, diverse, and challenging. … this is a book I heartily recommend to anyone wishing to learn or teach combinatorics." (Jeannette C. M. Janssen, SIAM Review, Vol. 26 (1), 2004)
"The author has covered a huge amount of ground in this book. … Each topic is covered in a way that takes the reader from the start right up to the most recent results in the area. … the book is clearly a ‘labour of love’. The author’s enthusiasm for the subject shines through page after page: it is hard not to feel his excitement as one reads what he has written." (Imre Leader, Combinatorics, Probability and Computing, Vol. 13, 2004)
"A text suitable for advanced undergraduate or graduate students. It begins with basics, inclusion-exclusion, pigeonhole, systems of distinct representatives. Substantial space is devoted to the more modern linear algebra and probabilistic methods. Algorithmic aspects permeate the book, making it suitable for a computer science, or jointmath/computer science course. There are numerous exercises." (J. Spencer, Mathematical Reviews, Issue 2003 g)
"Extremal Combinatorics is a part of finite mathematics … . The present book collects many different aspects of the field. It is wider than deep having 29 relatively short and independent chapters. These properties make the book accessible to a broad readership. … this volume also contains a large number of well chosen exercises of various range of difficulty. There is a useful home page edited by the author … . We warmly recommend this well-written and nicely edited book to anybody with combinatorial interest." (János Barát, Acta Scientiarum Mathematicarum, Vol. 68, 2002)
"This book presents several important parts of combinatorics with emphasis to methods for solving extremal problems. Some interesting applications in theoretical computer science are included. … As written in the preface, the text is indeed self-contained and the chapters are almost independent. More than 300 exercises … are included. The presentation is clear and sound. The book is not only valuable for students and teachers, but also for researchers working in discrete mathematics or theoretical computer science." (Konrad Engel, Zentralblatt MATH, Vol. 978, 2002)
Authors and Affiliations
Bibliographic Information
Book Title: Extremal Combinatorics
Book Subtitle: With Applications in Computer Science
Authors: Stasys Jukna
Series Title: Texts in Theoretical Computer Science. An EATCS Series
DOI: https://doi.org/10.1007/978-3-662-04650-0
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2001
eBook ISBN: 978-3-662-04650-0Published: 09 March 2013
Series ISSN: 1862-4499
Series E-ISSN: 1862-4502
Edition Number: 1
Number of Pages: XVII, 378
Topics: Discrete Mathematics in Computer Science, Probability Theory and Stochastic Processes, Mathematical Modeling and Industrial Mathematics, Combinatorics, Theory of Computation, Mathematical Logic and Foundations