论文标题
Penney的比赛与团体动作
The Penney's Game with Group Action
论文作者
论文摘要
考虑将字母$ \ MATHCAL {A} $与组动作配置，该操作将单词集分配到我们称为模式的等价类中。我们回答了彭尼（Penney）游戏的标准问题，并在图案上显示出游戏的非转换性，因为图案的长度往往是无穷大的。我们还分析了基于模式的Conway领先数字和预期等待时间的界限，并在循环和对称的小组动作下进一步探索了游戏。
Consider equipping an alphabet $\mathcal{A}$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the Penney's game on patterns and show non-transitivity for the game on patterns as the length of the pattern tends to infinity. We also analyze bounds on the pattern-based Conway leading number and expected wait time, and further explore the game under the cyclic and symmetric group actions.
