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arXiv 2201.06069math.CO
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发现一个新的普遍游击队规则

Discovering a new universal partizan ruleset

Koki Suetsugu

摘要:

在组合对策论中,我们研究对策集G,其元素由规则集的位置映射而成。在许多情况下,给定一个规则,不是G的所有元素都可以作为规则中的位置给出。什么样的规则会允许它们全部出现,这是一个耐人寻味的问题。本文引入了一个规则,称为转瓦规则,并证明了该规则是泛规则,即G中的每个元素都可以作为规则中的一个位置出现。这是继广义konane之后的第二个普适partizan规则。

英文摘要:

In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question what kind of ruleset would allow all of them to appear. In this paper, we introduce a ruleset named turning tiles and prove the ruleset is a universal partizan ruleset, that is, every element in G can occur as a position in the ruleset. This is the second universal partizan ruleset after generalized konane.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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