The Basis of Foot-Sortable Sock Orderings

Abstract: Defant and Kravitz considered the following problem: Suppose that, to the right of a foot, there is a line of colored socks that needs to be sorted. However, at any point in time, one can only either place the leftmost sock to the right of the foot onto the foot (stack) or remove the outermost sock on the foot and make it the rightmost sock to the left of the foot (unstack). In this paper, we explicitly describe all minimal initial sock orderings that are unsortable.