Woodslane | Book - 9781470467098

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Combinatorial Convexity

ISBN-13: 9781470467098
Publisher: AMERICAN MATHEMATICAL SOCIETY
Imprint: AMERICAN MATHEMATICAL SOCIETY
By Imre Barany
Price: AUD $142.00
Stock: 0 in stock
Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
Local release date: 29/05/2022
Format: Paperback (254.00mm X 178.00mm) 148 pages Weight: 294g
Categories: Geometry [PBM]

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Author Biography
Table of Contents
Reviews
Google Preview: This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Caratheodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Caratheodory, and the $(p, q)$ theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.; Imre Barany, Renyi Institute of Mathematics, Budapest, Hungary, and University College London, United Kingdom.; Basic concepts Caratheodory's theorem Radon's theorem Topological Radon Tverberg's theorem General position Helly's theorem Applications of Helly's theorem Fractional Helly Colourful Caratheodory Colourful Caratheodory again Colourful Helly Tverberg's theorem again Colourful Tverberg theorem Sarkaria and Kirchberger generalized The Erdos-Szekers theorem The same type lemma Better bound for the Erdos-Szekeres number Covering number, planar case The stretched grid Covering number, general case Upper bound on the covering number The point selection theorem Homogeneous selection Missing few simplices Weak $\varepsilon$-nets Lower bound on the size of weak $\varepsilon$-nets The $(p,q)$ theorem The colourful $(p,q)$ theorem $d$-intervals Halving lines, havling planes Convex lattice sets Fractional Helly for convex lattice sets Bibliography Index; This is an elegant, well written, concise treatment of an attractive and active subject, written by an expert who has made important contributions to the area himself. I am sure this will be a successful textbook."" -Noga Alon, Princeton University and Tel Aviv University ""I think this book is a gem."" -Janos Pach, Renyi Institute of Mathematics, Budapest; Google Preview content

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Combinatorial Convexity