Motivated by the study of affine Weyl groups, a ranked poset structure is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an interval in the affine symmetric group $\tilde S_n$ with the weak order. The poset is a semidistributive lattice, and the rank function, whose range is cubic in $n$, is computed by some special formula involving inversions. We prove also some links with Eulerian numbers, triangulations of an $n$-gon, and Young's lattice.
@article{10_37236_9982,
author = {Antoine Abram and Nathan Chapelier-Laget and Christophe Reutenauer},
title = {An order on circular permutations},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {3},
doi = {10.37236/9982},
zbl = {1542.06002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9982/}
}
TY - JOUR
AU - Antoine Abram
AU - Nathan Chapelier-Laget
AU - Christophe Reutenauer
TI - An order on circular permutations
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/9982/
DO - 10.37236/9982
ID - 10_37236_9982
ER -
%0 Journal Article
%A Antoine Abram
%A Nathan Chapelier-Laget
%A Christophe Reutenauer
%T An order on circular permutations
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/9982/
%R 10.37236/9982
%F 10_37236_9982
Antoine Abram; Nathan Chapelier-Laget; Christophe Reutenauer. An order on circular permutations. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9982
