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Princeton University Library Catalog
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Combinatorial convexity / Imre Bárány.
Author
Bárány, Imre
[Browse]
Format
Book
Language
English
Published/Created
Providence, Rhode Island : American Mathematical Society, [2021]
©2021
Description
viii, 148 pages : illustrations (some color) ; 26 cm.
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA640 .B37 2021
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Details
Subject(s)
Convex sets
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Combinatorial analysis
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Series
University lecture series (Providence, R.I.) ; 77.
[More in this series]
University lecture series, 1047-3998 ; volume 77
Summary note
"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, Carathéodory, 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 Carathéodory, 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"--Provided by publisher.
Bibliographic references
Includes bibliographical references and index.
Contents
Basic concepts
Carathéodory's theorem
Radon's theorem
Topological Radon
Tverberg's theorem
General position
Helly's theorem
Applications of Helly's theorem
Fractional Helly
Colourful Carathéodory
Colourful Carathéodory again
Colourful Helly
Tverberg's theorem again
Colourful Tverberg theorem
Sarkaria and Kirchberger generalized
The Erdős-Szekers theorem
The same type lemma
Better bound for the Erdős-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 e-nets
Lower bound on the size of weak e-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.
Show 30 more Contents items
ISBN
9781470467098 (paperback)
1470467097 (paperback)
LCCN
2021026891
OCLC
1262669540
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