English

The Basis of Foot-Sortable Sock Orderings

Combinatorics 2025-12-19 v3

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.

Keywords

Cite

@article{arxiv.2408.13938,
  title  = {The Basis of Foot-Sortable Sock Orderings},
  author = {Theodore Molla and Corey Nelson},
  journal= {arXiv preprint arXiv:2408.13938},
  year   = {2025}
}

Comments

20 pages. Accepted for publication in Discrete Mathematics