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Combinatorial Games
Edited by: Richard K. Guy, University of Calgary, Canada
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Proceedings of Symposia in Applied Mathematics
1991; 233 pp; softcover
Volume: 43
Reprint/Revision History:
reprinted 2000
ISBN-10: 0-8218-1925-9
ISBN-13: 978-0-8218-1925-8
List Price: US$48
Member Price: US$38.40
Order Code: PSAPM/43.S
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Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings in Columbus in August 1990, the ten papers in this volume will provide readers with insight into this exciting field. Because the book requires very little background, it will likely find a wide audience that includes the amateur interested in playing games, the undergraduate looking for a new area of study, instructors seeking a refreshing area in which to give new courses at both the undergraduate and graduate levels, and graduate students looking for a variety of research topics.

In the opening paper, Guy contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. Conway introduces a new theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the theory of games. Guy describes impartial games, with the same options for both players, and the Sprague-Grundy theory. Conway discusses a variety of ways in which games can be played simultaneously. Berlekamp uses the theory of "hot" games to make remarkable progress in the analysis of Go Endgames. Pless demonstrates the close connection between several impartial games and error-correcting codes. Fraenkel explains the way in which complexity theory is very well illustrated by combinatorial games, which supply a plethora of examples of harder problems than most of those which have been considered in the past. Nowakowski outlines the theory of three particular games--Welter's Game, Sylver Coinage, and Dots-and-Boxes. A list of three dozen open problems and a bibliography of 400 items are appended.

Reviews

"Constitutes a very good short course on the subject of combinatorial games ... a series of eight introductory papers, well chosen and fitting well together. The result is an informative and readable text, useful both for those who want to get acquainted with the basics and for those interested in some special attractive topics in the area."

-- Mathematical Reviews

Table of Contents

  • R. K. Guy -- What is a game?
  • J. H. Conway -- Numbers and games
  • R. K. Guy -- Impartial games
  • J. H. Conway -- More ways of combining games
  • E. R. Berlekamp -- Introductory overview of mathematical go endgames
  • V. Pless -- Games and codes
  • A. S. Fraenkel -- Complexity of games
  • R. J. Nowakowski -- ..., Welter's game, Sylver coinage, dots-and-boxes, ...
  • R. K. Guy -- Unsolved problems in combinatorial games
  • A. S. Fraenkel -- Selected bibliography on combinatorial games and some related material
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