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· 제목 : Combinatorial Convexity (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 기하학 일반
· ISBN : 9781470467098
· 쪽수 : 148쪽
· 출판일 : 2022-02-28
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 기하학 일반
· ISBN : 9781470467098
· 쪽수 : 148쪽
· 출판일 : 2022-02-28
목차
- 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
