عنوان

Extremal problems for finite sets /

1470440393

9781470440398

Extremal problems for finite sets /

[Book]

Peter Frankl, Norihide Tokushige.

Providence, Rhode Island :

American Mathematical Society,

[2018]

viii, 224 pages ;

22 cm.

Student mathematical library ;

volume 86

Includes bibliographical references and index.

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 s 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. r-Cross union families -- Chapter 15. Random walk method -- Chapter 16. L-systems -- Chapter 17. Exponent of a (10, {0, 1, 3, 6})-system -- Chapter 18. The Deza-Erd˝os-Frankl Theorem -- Chapter 19. F¨uredi's structure theorem -- Chapter 20. R¨odl'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 L-systems -- Chapter 25. Oddtown and eventown problems -- Chapter 26. Tensor product method -- Chapter 27. The ratio bound -- Chapter 28. Measures of cross independent sets -- Chapter 29. Application of semidefinite programming -- Chapter 30. A cross intersection problem with measures -- Chapter 31. Capsets and sunflowers -- Chapter 32. Challenging open problems.

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"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." --

Extremal problems (Mathematics)

Set theory.

Combinatorics -- Extremal combinatorics -- Extremal set theory.

Combinatorics -- Instructional exposition (textbooks, tutorial papers, etc.).

Extremal problems (Mathematics)

Set theory.

Frankl, P., (Peter),1953-

Tokushige, Norihide,1963-

20200823025813.0

rda

[Book]

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