论文标题
原子重量和二聚体的组合游戏
Atomic weights and the combinatorial game of Bipass
论文作者
论文摘要
我们在正常游戏组合游戏的框架内定义了一个全小规则集，即bipass。游戏在有限的黑白石头上玩。如果它们不绕过自己的一种，则交换了不同颜色的石头。我们发现从条带到整数原子重量（Berlekamp，Conway and Guy 1982）的溢出功能，该功能衡量了全小游戏中的单元数量。该结果为许多游戏提供了明确的获胜策略，在没有的情况下，它为规范表单游戏值提供了狭窄的界限。我们证明游戏值 *2并未作为二键的分离总和。此外，我们找到了某些参数化游戏系列的游戏值，包括无限数量的价值条 *。
We define an all-small ruleset, Bipass, within the framework of normal-play combinatorial games. A game is played on finite strips of black and white stones. Stones of different colors are swapped provided they do not bypass one of their own kind. We find a surjective function from the strips to integer atomic weights (Berlekamp, Conway and Guy 1982) that measures the number of units in all-small games. This result provides explicit winning strategies for many games, and in cases where it does not, it gives narrow bounds for the canonical form game values. We prove that the game value *2 does not appear as a disjunctive sum of Bipass. Moreover, we find game values for some parametrized families of games, including an infinite number of strips of value *.
