The insertion encoding of Cayley permutations
Combinatorics
2026-04-30 v2
Abstract
We introduce the vertical and horizontal insertion encodings for Cayley permutations which naturally generalise the insertion encoding for permutations. In both cases, we fully classify the Cayley permutation classes for which these languages are regular, and provide an algorithm for computing the rational generating functions. We use our algorithm to solve an open problem of Cerbai by enumerating the hare pop-stack sortable Cayley permutations.
Cite
@article{arxiv.2505.08480,
title = {The insertion encoding of Cayley permutations},
author = {Christian Bean and Paul C. Bell and Abigail Ollson},
journal= {arXiv preprint arXiv:2505.08480},
year = {2026}
}