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

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Table of Contents

Front/Back Matter

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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

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