Read more
Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.
List of contents
1. About this book Urban Larsson; 2. Temperatures of games and coupons Elwyn Berlekamp; 3. Wythoff visions Eric Duchêne, Aviezri Fraenkel, Vladimir Gurvich, Nhan Ho, Clark Kimberling and Urban Larsson; 4. Scoring games: the state of play Urban Larsson, Richard Nowakowski and Carlos Pereira dos Santos; 5. Restricted developments in partizan misère game theory Rebecca Milley and Gabriel Renault; 6. Unsolved problems in combinatorial games Richard Nowakowski; 7. Misère games and misère quotients Aaron Siegel; 8. An historical tour of binary and tours David Singmaster; 9. A note on polynomial profiles of placement games J. I. Brown, D. Cox, A. Hoefel, Neil McKay, Rebecca Milley, Richard Nowakowski and Angela A. Siegel; 10. A PSPACE-complete Graph Nim Kyle Burke and Olivia George; 11. A nontrivial surjective map onto the short Conway group Alda Carvalho and Carlos Pereira dos Santos; 12. Games and complexes I: transformation via ideals Sara Faridi, Svenja Huntemann and Richard Nowakowski; 13. Games and complexes II: weight games and Kruskal-Katona type bounds Sara Faridi, Svenja Huntemann and Richard Nowakowski; 14. Chromatic Nim finds a game for your solution Mike Fisher and Urban Larsson; 15. Take-away games on Beatty's theorem and the notion of k-invariance Aviezri Fraenkel and Urban Larsson; 16. Geometric analysis of a generalized Wythoff game Eric Friedman, Scott M. Garrabrant, Ilona Phipps-Morgan, Adam S. Landsberg and Urban Larsson; 17. Searching for periodicity in officers J. P. Grossman; 18. Good pass moves in no-draw HyperHex: two proverbs Ryan Hayward; 19. Conjoined games: Go-Cut and Sno-Go Melissa Huggan and Richard Nowakowski; 20. Impartial games whose rulesets produce continued fractions Urban Larsson and Mike Weimerskirch; 21. Endgames in bidding chess Urban Larsson and Johan Wastlund; 22. Phutball draws Sucharit Sarkar; 23. Scoring play combinatorial games Fraser Stewart; 24. Generalized misère play Mike Weimerskirch.
About the author
Urban Larsson is a postdoctoral fellow at the Industrial Engineering and Management department at Technion – Israel Institute of Technology, Haifa. Prior to this he was a Killam postdoctoral fellow at Dalhousie University, Canada 2014-2016, and before that he was a Lecturer 2013–2014 and a Ph.D. student (ending 2013) at Chalmers tekniska högskola and Göteborgs universitet, Sweden. His main research areas are game theory, number theory, computer science and algorithms.
Summary
This book surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information. Topics include scoring, bidding chess, Wythoff Nim, misère play, partizan bidding, loopy games, and placement games, along with a survey of temperature theory by Elwyn Berlekamp and a list of unsolved problems.
