Unknotted cycles
Combinatorics
2020-07-10 v1 Geometric Topology
Abstract
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which correspond in this way to an unknot are enumerated by the Schr\"{o}der numbers, and also enumerate the permutations corresponding to an unlink. The proof uses Bennequin's inequality.
Keywords
Cite
@article{arxiv.2007.04917,
title = {Unknotted cycles},
author = {Christopher R. Cornwell and Nathan McNew},
journal= {arXiv preprint arXiv:2007.04917},
year = {2020}
}