Extremal Problems for Finite Sets
About this Title
Peter Frankl, Rényi Institute, Budapest, Hungary and Norihide Tokushige, Ryukyu University, Okinawa, Japan
Publication: The Student Mathematical Library
Publication Year:
2018; Volume 86
ISBNs: 978-1-4704-4039-8 (print); 978-1-4704-4847-9 (online)
DOI: https://doi.org/10.1090/stml/086
MathSciNet review: MR3822342
MSC: Primary 05-01; Secondary 05D05
Table of Contents
Front/Back Matter
Chapters
- Introduction
- Operations on sets and set systems
- Theorems on traces
- The Erdős-Ko-Rado theorem via shifting
- Katona’s circle
- The Kurskal-Katona theorem
- Kleitman theorem for no $s$ pairwise disjoint sets
- The Hilton-Milner theorem
- The Erdős matching conjecture
- The Ahswede-Khachatrian theorem
- Pushing-pulling method
- Uniform measure versus product measure
- Kleitman’s correlation inequality
- $r$-cross union families
- Random walk method
- $L$-systems
- Exponent of $(10,\{0,1,3,6\})$-system
- The Deza-Erdős-Frankl theorem
- Füredi’s structure theorem
- Rödl’s packing theorem
- Upper bounds using multilinear polynomials
- Application to discrete geometry
- Upper bounds using inclusion matrices
- Some algebraic constructions for $L$-systems
- Oddtown and eventown problems
- Tensor product method
- The ratio bound
- Measures of cross independent sets
- Application of semidefinite programming
- A cross intersection problem with measures
- Capsets and sunflowers
- Challenging open problems