5 D ec 2 00 6 Misère Quotients for 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
2 M ar 2 00 7 The Structure and Classification of Misère Quotients
A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...
متن کاملMisère Quotients of 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....
متن کاملMisère quotients for impartial games
We announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure theory of misère quotients, including a connection between the combinatorial structure of normal and misère play.
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This appendix contains detailed solutions to many of the games discussed in Appendix A. Figure 1 summarizes the status of every octal game with at most three code digits. For each game Γ, the chart indicates whether Γ is tame or wild, and whether its normaland/or misère-play solution is known. Figures 2 and 4 present complete solutions to wild twoand three-digit octal games with relatively simp...
متن کاملThe structure and classificationof misère quotients
A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...
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