规则集产生给定连分数的公平博弈
Impartial games whose rulesets produce given continued fractions
摘要：
我们研究2人公平的游戏的形式带走产生的P-位置（第二个玩家获胜的位置）对应于互补的贝蒂序列，由连分数（1; k，1，k，1，.）和（k+1; k，1，k，1，...）。我们的问题是相反的主要研究领域在这一领域，这是，给定一个游戏，了解其P-位置集。相反，我们给出了一组（候选）P-位置，并寻找“简单”规则。我们的规则满足两个标准，它们是由一个闭公式给出的，并且它们是不变的，也就是说，可用的移动不依赖于所处的位置（对于所有具有非负坐标的选项）。
英文摘要：
We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our problem is the opposite of the main field of research in this area, which is to, given a game, understand its set of P-positions. We are rather given a set of (candidate) P-positions and look for "simple" rules. Our rules satisfy two criteria, they are given by a closed formula and they are invariant, that is, the available moves do not depend on the position played from (for all options with non-negative coordinates).
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。
