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Inevitable Randomness in Discrete Mathematics
About this Title
József Beck, Rutgers, The State University of New Jersey, Piscataway, NJ
Publication: University Lecture Series
Publication Year:
2009; Volume 49
ISBNs: 978-0-8218-4756-5 (print); 978-1-4704-1644-7 (online)
DOI: https://doi.org/10.1090/ulect/049
MathSciNet review: MR2543141
MSC: Primary 60C05; Secondary 05D10, 11K38, 60F05, 68Q87, 91A46
Table of Contents
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Front/Back Matter
Part A. Reading the shadows on the wall and formulating a vague conjecture
- Chapter 1. Complex systems
- Chapter 2. Collecting data: Apparent randomness of digit sequences
- Chapter 3. Collecting data: More randomness in number theory
- Chapter 4. Laplace and the principle of insufficient reason
- Chapter 5. Collecting proofs for the SLG conjecture
Part B. More evidence for the SLG conjecture: Exact solutions in real game theory
- Chapter 6. Ramsey theory and games
- Chapter 7. Practice session (I): More on Ramsey games and strategies
- Chapter 8. Practice session (II): Connectivity games and more strategies
- Chapter 9. What kind of games?
- Chapter 10. Exact solutions of games: Understanding via the equiprobability postulate
- Chapter 11. Equiprobability postulate with constraints (endgame policy)
- Chapter 12. Constraints and threshold clustering
- Chapter 13. Threshold clustering and a few bold conjectures
Part C. New evidence: Games and graphs, the surplus, and the square root law
- Chapter 14. Yet another simplification: Sparse hypergraphs and the surplus
- Chapter 15. Is surplus the right concept? (I)
- Chapter 16. Is surplus the right concept? (II)
- Chapter 17. Working with a game-theoretic partition function
- Chapter 18. An attempt to save the variance
- Chapter 19. Proof of theorem 1: Combining the variance with an exponential sum
- Chapter 20. Proof of theoem 2: The upper bound
- Chapter 21. Conclusion (I): More on theorem 1
- Chapter 22. Conclusion (II): Beyond the SLG conjecture