A path formula for the sock sorting problem

preprint2020arXivOpen access

Abstract

Suppose nn 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 2n2n socks is taken from the dryer and give an explicit formula for the probability that this sequence equals a given sequence of length 2n2n.

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