Items related to Extremal Combinatorics: With Applications in Computer...
Synopsis
Prolog: What This Book Is About.- Notation.- 1. Counting.- 2. Advanced Counting.- 3. The Principle of Inclusion and Exclusion.- 4. The Pigeonhole Principle.- 5. Systems of Distinct Representatives.- 6. Colorings.- 7. Sunflowers.- 8. Intersecting Families.- 9. Chains and Antichains.- 10. Blocking Sets and the Duality.- 11. Density and Universality.- 12. Witness Sets and Isolation.- 13. Designs.- 14. The Basic Method.- 15. Orthogonality and Rank Arguments.- 16. Span Programs.- 17. Basic Tools.- 18. Counting Sieve.- 19. The Lovász Sieve.- 20. Linearity of Expectation.- 21. The Deletion Method.- 22. The Second Moment Method.- 23. The Entropy Function.- 24. Random Walks.- 25. Randomized Algorithms.- 26. Derandomization.- 27. Ramsey's Theorem.- 28. Ramseyan Theorems for Numbers.- 29. The Hales-Jewett Theorem.- Epilog: What Next?.- References.- Name Index.
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