Extremal Problems for Finite Sets
eBook - PDF

Extremal Problems for Finite Sets

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Extremal Problems for Finite Sets

About this book

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 elegance and power of this field of study.The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede–Khachatrian theorem as well as some recent progress on the Erd?s matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza–Erd?s–Frankl theorem, application of Rödl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erd?s–SzemerĂ©di sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Extremal Problems for Finite Sets by Peter Frankl,Norihide Tokushige in PDF and/or ePUB format, as well as other popular books in Mathematics & Discrete Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title page
  3. Contents
  4. Notation
  5. Chapter 1. Introduction
  6. Chapter 2. Operations on sets and set systems
  7. Chapter 3. Theorems on traces
  8. Chapter 4. The ErdƑs–Ko–Rado Theorem via shifting
  9. Chapter 5. Katona’s circle
  10. Chapter 6. The Kruskal–Katona Theorem
  11. Chapter 7. Kleitman Theorem for no 𝑠 pairwise disjoint sets
  12. Chapter 8. The Hilton–Milner Theorem
  13. Chapter 9. The ErdƑs matching conjecture
  14. Chapter 10. The Ahlswede–Khachatrian Theorem
  15. Chapter 11. Pushing-pulling method
  16. Chapter 12. Uniform measure versus product measure
  17. Chapter 13. Kleitman’s correlation inequality
  18. Chapter 14. 𝑟-Cross union families
  19. Chapter 15. Random walk method
  20. Chapter 16. 𝐿-systems
  21. Chapter 17. Exponent of a (10,{0,1,3,6})-system
  22. Chapter 18. The Deza–ErdƑs–Frankl Theorem
  23. Chapter 19. FĂŒredi’s structure theorem
  24. Chapter 20. Rödl’s packing theorem
  25. Chapter 21. Upper bounds using multilinear polynomials
  26. Chapter 22. Application to discrete geometry
  27. Chapter 23. Upper bounds using inclusion matrices
  28. Chapter 24. Some algebraic constructions for 𝐿-systems
  29. Chapter 25. Oddtown and eventown problems
  30. Chapter 26. Tensor product method
  31. Chapter 27. The ratio bound
  32. Chapter 28. Measures of cross independent sets
  33. Chapter 29. Application of semidefinite programming
  34. Chapter 30. A cross intersection problem with measures
  35. Chapter 31. Capsets and sunflowers
  36. Chapter 32. Challenging open problems
  37. Bibliography
  38. Index
  39. Back Cover