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 Schröder numbers, and also enumerate the permutations corresponding to an unlink. The proof uses Bennequin's inequality.
@article{10_37236_11016,
author = {Christopher Cornwell and Nathan McNew},
title = {Unknotted cycles},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/11016},
zbl = {1504.05009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11016/}
}
TY - JOUR
AU - Christopher Cornwell
AU - Nathan McNew
TI - Unknotted cycles
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/11016/
DO - 10.37236/11016
ID - 10_37236_11016
ER -
%0 Journal Article
%A Christopher Cornwell
%A Nathan McNew
%T Unknotted cycles
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/11016/
%R 10.37236/11016
%F 10_37236_11016
Christopher Cornwell; Nathan McNew. Unknotted cycles. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/11016
