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arXiv · 2312.14397

Deciding Foot-sortability and Minimal 2-bounded Non-foot-sortable Sock Orderings

Hung-Hsun Hans Yu
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Abstract

A sock ordering is a sequence of socks with different colors. A sock ordering is foot-sortable if the sequence of socks can be sorted by a stack so that socks with the same color form a contiguous block. The problem of deciding whether a given sock ordering is foot-sortable was first considered by Defant and Kravitz, who resolved the case for alignment-free 2-uniform sock orderings. In this paper, we resolve the problem in a more general setting, where each color appears in the sock ordering at most twice. A key component of the argument is a fast algorithm that determines the foot-sortability of a sock ordering of length $N$ in time $O(N\log N)$, which is also an interesting result on its own.

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Hung-Hsun Hans Yu. 2023-12-22. Deciding Foot-sortability and Minimal 2-bounded Non-foot-sortable Sock Orderings. https://arxiv.org/abs/2312.14397

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