Combinatorial Convexity

ISBN-13: 9781470467098 / Miękka / 2022 / 148 str.

Imre Barany

Spis treści

• 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