Combinatorial Convexity

Imre Barany, Renyi Institute of Mathematics, Budapest, Hungary, and University College London, United Kingdom.

• Basic conceptsCaratheodory's theoremRadon's theoremTopological RadonTverberg's theoremGeneral positionHelly's theoremApplications of Helly's theoremFractional HellyColourful CaratheodoryColourful Caratheodory againColourful HellyTverberg's theorem againColourful Tverberg theoremSarkaria and Kirchberger generalizedThe Erdos-Szekers theoremThe same type lemmaBetter bound for the Erdos-Szekeres numberCovering number, planar caseThe stretched gridCovering number, general caseUpper bound on the covering numberThe point selection theoremHomogeneous selectionMissing few simplicesWeak $\varepsilon$-netsLower bound on the size of weak $\varepsilon$-netsThe $(p,q)$ theoremThe colourful $(p,q)$ theorem$d$-intervalsHalving lines, havling planesConvex lattice setsFractional Helly for convex lattice setsBibliographyIndex

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