This collection of 22 research papers and state-of-the-art surveys extends the subseries 'Games of No Chance' pioneered in 1996. Survey topics include Richman bidding combinatorial games, classical subtraction games and absolute additive theory. Other topics discussed include extensions of normal play theory such as Absolute CGT and Affine normal play; additive theory; aspects of generic impartial games arising from the study of nim-values; dead-ending misčre reduction theorems; Wythoff-type variations; complexity issues; and aspects of classical games including a rigorous justification of the celebrated result that king, bishop and knight can checkmate a lonely king on an arbitrarily large chessboard. The recurring list of open problems, updated and annotated, will interest all practitioners of CGT and related fields including algebra, computer science, combinatorics, number theory and classical game theory.
Recenzijos
'Games of No Chance are games with perfect information like Chess (about which chapter 15 says something new). They were pioneered by the renowned mathematicians Berlekamp, Conway and Guy. This volume demonstrates how this original and playful but serious branch of mathematics flourishes and grows.' Bernhard von Stengel, London School of Economics and Political Science
Daugiau informacijos
Discover the tools required to learn how to win (even more) games by seeing the underlying mathematical structure.
Preface Urban Larsson;
1. Combinatorial game theory monoids and their
absolute restrictions: a survey Alfie M. Davies, Urban Larsson, Rebecca
Milley, Richard J. Nowakowski, Carlos P. Santos and Aaron N. Siegel;
2. A
brief conversation about subtraction games Urban Larsson, Indrajit Saha and
Koki Suetsugu;
3. Survey on Richman bidding combinatorial games Prem Kant and
Urban Larsson;
4. Unsolved problems in combinatorial games Richard J.
Nowakowski;
5. Absolute combinatorial game theory Urban Larsson, Richard J.
Nowakowski and Carlos P. Santos;
6. Affine normal play Urban Larsson, Richard
J. Nowakowski and Carlos P. Santos;
7. On the general dead-ending universe of
partizan games Aaron N. Siegel;
8. Infinitely many absolute universes Urban
Larsson, Richard J. Nowakowski and Carlos P. Santos;
9. Reversibility,
canonical form, and invertibility in dead-ending misčre play Urban Larsson,
Rebecca Milley, Richard J. Nowakowski, Gabriel Renault and Carlos P. Santos;
10. Dead-ending day-2 games under misčre play Aaron Dwyer, Rebecca Milley and
Michael Willette;
11. All passable games are realizable as monotone set
coloring games Eric Demer, Peter Selinger and Kyle Wang;
12. Values of
generic impartial combinatorial games Eric Friedman;
13. A family of Nim-like
arrays: stabilization Lowell Abrams and Dena S. Cowen-Morton;
14. Memgames
Urban Larsson, Simon Rubinstein-Salzedo and Aaron N. Siegel;
15. The bishop
and knight checkmate on a large chessboard Johan Wästlund;
16. An update on
the coin-moving game on the square grid Florian Galliot, Sylvain Gravier and
Isabelle Sivignon;
17. P play in Candy Nim Nitya Mani, Rajiv Nelakanti, Simon
Rubinstein-Salzedo and Alexa Tholen;
18. Keeping your distance is hard Kyle
Burke, Silvia Heubach, Melissa A. Huggan and Svenja Huntemann;
19. Improving
upper and lower bounds of the number of games born by day 4 Koki Suetsugu;
20. Lexicographic Wythoff David Klein and Aviezri S. Fraenkel;
21. Corner the
empress Robbert Fokkink, Gerard Francis Ortega and Dan Rust;
22. m-modular
Wythoff Tanya Khovanova and Nelson Niu.
Urban Larsson is an associate professor at the Department of Industrial Engineering and Operations Research at the Indian Institute of Technology, Bombay, India. He is a worldwide researcher and teacher in combinatorial game theory, and organizes workshops and conferences on this subject. He has won awards such as the Killam Fellowship, and he is the editor of the volumes 'Games of No Chance 5' (2019), and IJGT's 'Special Issues on Combinatorial Game Theory' (2018 and 2025). He publishes regularly in the top journals of the field, with 24 accepted/published papers in the last five years, and he has more than 50 co-authors.
