论文标题
卡片和$ P $ - 分区
Card shuffling and $P$-partitions
论文作者
论文摘要
在这篇说明性文章中，我们重点介绍了卡片改组与称为$ p $ - 分区的功能之间的直接连接，这些功能来自代数组合。尽管我们讨论的结果中的许多（但不是全部）是已知的，但我们提供了统一的处理。关键的想法是：从货架上获得置换$π$的可能性是，随机$ p $ - 分区由$π$排序，并且从riffle Shuffling获得$π$的可能性是随机$ p $ - 分支由$π^^{ - 1} $排序的可能性。
In this expository article, we highlight the direct connection between card shuffling and the functions known as $P$-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a unified treatment. The key idea is this: the probability of obtaining a permutation $π$ from shelf shuffling is the probability that a random $P$-partition is sorted by $π$, and the probability of obtaining $π$ from riffle shuffling is the probability that a random $P$-partition is sorted by $π^{-1}$.
