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Extremal problems for finite sets

Author: P Frankl; Norihide Tokushige
Publisher: Providence, Rhode Island : American Mathematical Society, [2018]
Series: Student mathematical library, v. 86.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2017061643
(OCoLC)1021054967
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: P Frankl; Norihide Tokushige
ISBN: 9781470448479 1470448475
OCLC Number: 1050364600
Description: 1 online resource.
Contents: Cover; Title page; Contents; Notation; Chapter 1. Introduction; Chapter 2. Operations on sets and set systems; Chapter 3. Theorems on traces; Chapter 4. The Erdős-Ko-Rado Theorem via shifting; Chapter 5. Katona's circle; Chapter 6. The Kruskal-Katona Theorem; Chapter 7. Kleitman Theorem for no pairwise disjoint sets; Chapter 8. The Hilton-Milner Theorem; Chapter 9. The Erdős matching conjecture; Chapter 10. The Ahlswede-Khachatrian Theorem; Chapter 11. Pushing-pulling method; Chapter 12. Uniform measure versus product measure; Chapter 13. Kleitman's correlation inequality. Chapter 14.-Cross union familiesChapter 15. Random walk method; Chapter 16.-systems; Chapter 17. Exponent of a (10,{0,1,3,6})-system; Chapter 18. The Deza-Erdős-Frankl Theorem; Chapter 19. Füredi's structure theorem; Chapter 20. Rödl's packing theorem; Chapter 21. Upper bounds using multilinear polynomials; Chapter 22. Application to discrete geometry; Chapter 23. Upper bounds using inclusion matrices; Chapter 24. Some algebraic constructions for -systems; Chapter 25. Oddtown and eventown problems; Chapter 26. Tensor product method; Chapter 27. The ratio bound. Chapter 28. Measures of cross independent setsChapter 29. Application of semidefinite programming; Chapter 30. A cross intersection problem with measures; Chapter 31. Capsets and sunflowers; Chapter 32. Challenging open problems; Bibliography; Index; Back Cover.
Series Title: Student mathematical library, v. 86.
Responsibility: Peter Frankl, Norihide Tokushige.

Abstract:

One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a  Read more...

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