Combinatorial Convexity
About this Title
Imre Bárány, Rényi Institute of Mathematics, Budapest, Hungary
Publication: University Lecture Series
Publication Year:
2021; Volume 77
ISBNs: 978-1-4704-6709-8 (print); 978-1-4704-6768-5 (online)
DOI: https://doi.org/10.1090/ulect/077
Table of Contents
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Front/Back Matter
Chapters
- 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 $\varepsilon$-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
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