AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

Front/Back Matter

• View this volume's front and 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