论文标题
袜子的脚步
Foot-Sorting for Socks
论文作者
论文摘要
如果您的袜子从洗衣服中出来，您应该如何对它们进行分类？我们介绍和研究一种新型的脚部排序算法，该算法使用脚试图对袜子排序进行分类。人们可以将此算法视为Knuth的堆叠算法的类似物，用于固定分区。可以使用固定脚的袜子订购的特征是克拉萨尔的固定分区图案遏制概念。我们提供涉及纤维纳acci数字的枚举，该数字在自然繁华的班级中的$ 1 $ foot-foot-foot-fot-fot的袜子订购。我们还证明，如果您有$ n $不同的颜色的袜子，那么您总是可以使用最多使用$ \ weft \ lceil \ log_2（n）\ right \ rceil $ fet对它们进行排序，我们使用Ramsey理论论点来表明此绑定是紧密的。
If your socks come out of the laundry all mixed up, how should you sort them? We introduce and study a novel foot-sorting algorithm that uses feet to attempt to sort a sock ordering; one can view this algorithm as an analogue of Knuth's stack-sorting algorithm for set partitions. The sock orderings that can be sorted using a fixed number of feet are characterized by Klazar's notion of set partition pattern containment. We give an enumeration involving Fibonacci numbers for the $1$-foot-sortable sock orderings within a naturally-arising class. We also prove that if you have socks of $n$ different colors, then you can always sort them using at most $\left\lceil\log_2(n)\right\rceil$ feet, and we use a Ramsey-theoretic argument to show that this bound is tight.
