Misère Quotients of Impartial Games
نویسندگان
چکیده
The G-values of various games, by R. K. Guy and C. A. B. Smith, introduced a broad class of impartial games and gave complete normalplay solutions for many of them. In this paper, we announce misère-play solutions to many of the games considered by Guy and Smith. They are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. Our solutions were obtained through a combination of theoretical advances and new algorithms for calculating misère quotients. We also introduce a structure theory for misère quotients and pose many open problems.
منابع مشابه
5 D ec 2 00 6 Misère Quotients for Impartial Games
The G-values of various games, by R. K. Guy and C. A. B. Smith, introduced a broad class of impartial games and gave complete normalplay solutions for many of them. In this paper, we announce misère-play solutions to many of the games considered by Guy and Smith. They are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games....
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