Combinatorial games
Author(s)
Bibliographic Information
Combinatorial games
（Proceedings of symposia in applied mathematics, v. 43 . AMS Short course lecture notes）
American Mathematical Society, c1991
Available at / 35 libraries
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Research Institute for Economics & Business Administration (RIEB) Library , Kobe University図書
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
"Lecture notes prepared for the American Mathematical Society Short Course [on] Combinatorial Games held in Columbus, Ohio, August 6-7, 1990" -- T.p.verso
Includes bibliographical references (p. 197-220) and index
Description and Table of Contents
Description
"The subject of combinatorics is only slowly acquiring respectability and combinatorial games will clearly take longer than the rest of combinatorics. Perhaps this partly stems from the puritanical view that anything amusing can't possibly involve any worthwhile mathematics." from the Preface. Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings , the ten papers in this volume will provide readers with insight into this exciting new field. (BULLET) 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, 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 demostrates 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 bibliography of 400 items are appended.
Table of Contents
- Richard K Guy, What is a game?
- John Horton Conway, Numbers and games
- Richard K Guy, Impartial games
- John Horton Conway, More ways of combining games
- Elwyn R Berlekamp, Introductory overview of mathematical go endgames
- Vera Pless, Games and codes
- Aviezri S Fraenkel, Complexity of games
- Richard J Nowakowski, Welter's games, Sylver coinage, dots-and-boxes
- Richard K Guy, Unsolved problems in combinatorial games
- Avierzri S Fraenkel, Selected bibliography on combinatorial games and some related material.
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