论文标题
袜子排序问题的路径公式
A path formula for the sock sorting problem
论文作者
论文摘要
假设$ n $不同的袜子放在滚筒式干衣机中。当烘干机完成的袜子被一个接一个地取出时，如果袜子匹配排序桌上的袜子之一，则拆下了两者，否则将其放在桌子上，直到其伴侣从干衣机出来为止。我们注意到桌子上的袜子数量是从干衣机中取出的$ 2N $袜子后的，并为此序列等于给定的长度$ 2N $的概率提供明确的公式。
Suppose $n$ different pairs of socks are put in a tumble dryer. When the dryer is finished socks are taken out one by one, if a sock matches one of the socks on the sorting table both are removed, otherwise it is put on the table until its partner emerges from the dryer. We note the number of socks on the table after each of the $2n$ socks is taken from the dryer and give an explicit formula for the probability that this sequence equals a given sequence of length $2n$.
