Extremal Finite Set Theory

ISBN-13: 9781138197848 / Angielski / Twarda / 2018 / 336 str.

Daniel Gerbner; Balazs Patkos

Opis

Extremal Finite Set Theory surveys old and new results in this subject. It presents an overview of the main techniques and tools (shifting, cycle method, profile polytopes, incidence matrices, combinatorial nullstellensatz, etc.) used in the different subtopics. 

Recenzje

 

"Materials collected in this book were meant to be presented at the Extremal Sets Systems Seminar of the Alfréd Rényi Institute of Mathematics. The main focus is placed on maximizing the cardinality of a family of sets satisfying some prescribed properties. The authors pay great attention to present a large range of proof techniques used in dealing with finite sets systems and give an extensive survey of recent results. Although ordinary graphs are 2-uniform families, extremal graph theory is outside the scope of this book. Ramsey-type theorems and coding theory are also avoided. The intended audience includes (1) students eager to learn the central topics on a graduate level; (2) university professors offering courses on extremal combinatorics; (3) researchers refreshing their knowledge and learning recent developments in the field. The book concludes with a comprehensive bibliography of 556 items. This makes it a convenient reference book for people interested in the latest developments in extremal finite set theory."

Ko-Wei Lih (Taipei) zbMath September 2019

"This book gives a well-organized and timely summary of research directions in classical extremal combinatorics. As the title clari es, the focus excludes in nitary combinatorics. And, by the authors' own admission, results particular to extremal graph theory or coding theory are omitted. Instead, a considerable level of depth is o
ered on the status of the primary topics of extremal set theory: intersection theorems, Sperner families, Tur□an problems, and saturation variants of these. The text is appropriate for graduate students or keen undergrads, and serves equally well as a comprehensive reference for researchers.

The book has over 500 insightful exercises which build on the presentation. These are especially valuable for young researchers in the subject, who can gain familiarity with the methods and connect various topics."

~Peter James Dukes--Mathematical Reviews Oct. 2019