Misère quotients for impartial games
نویسندگان
چکیده
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.
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....
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 کامل2 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 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...
متن کامل7 Misère Canonical Forms of Partizan Games
We show that partizan games admit canonical forms in misère play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and misère-play impartial games. It is fully constructive, and algorithms readily emerge for comparing misère games and calculating their canonical forms. We use these techniques to show that there are precisely 256 games born by day 2, and to ...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 115 شماره
صفحات -
تاریخ انتشار 2008