公平游戏的拆分和的若干结果
Some results on split sum of impartial games
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中文总结 AI 辅助
本文针对带通过的Nim游戏这一组合游戏难题，扩展拆分和的应用，明确其与经典析取和的等价情形，推广Grundy值并揭示其在拆分和下的不同性质，为公平游戏研究提供新结果。
中文摘要 AI 辅助
如《组合游戏中的未解决问题》中问题A13所述，带通过的Nim游戏是一个难题。Nim是最早被解决的组合游戏之一，但引入通过后游戏变得复杂得多。本文扩展了《带通过的公平游戏研究》中引入的拆分和的应用，找到了拆分和与经典析取和表现相同的情况。我们还为拆分和引入了Grundy值的推广，发现具有相同Grundy值的游戏在拆分和下可呈现截然不同的性质。
英文摘要
As it is stated in "Unsolved problems in combinatorial games" as problem A13, Nim with pass is a difficult problem. Nim was one of the first combinatorial games to be solved but when we introduce a pass the game becomes far more complex. In this article we extend the use of the split sum introduced in "Investigations of Impartial Games With a Pass" and we find cases where the split sum act the same as an classical disjunctive sum. We also introduce generalization of Grundy value for the split sum and find that games of same Grundy values can give very different properties with a split sum.
