منابع مشابه
Misère 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.
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 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 ...
متن کاملMist&-e Annihilation Games*
Graph games with an annihilation rule, as introduced by Conway, Fraenkel and Yesha, are studied under the midre play rule for progressively finite graphs that satisfy a condition on the reversibility of non-terminal Sprague-Grundy zeros to Spragu+Grundy ones. Two general theorems on the Spragu+Grundy zeros and ones are given, followed by two theorems characterizing the set of P-positions under ...
متن کاملDicots, and a taxonomic ranking for misère games
We study combinatorial games in misère version. In a general context, little can be said about misère games. For this reason, several universes were earlier considered for their study, which can be ranked according to their inclusion ordering. We study in particular a special universe of games called dicots, which turns out to be the known universe of lowest rank modulo which equivalence in mis...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1984
ISSN: 0097-3165
DOI: 10.1016/0097-3165(84)90046-3