We give a $q$-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this $q$-analogue exhibits the cyclic sieving phenomenon under a natural action of the cyclic group. The enumeration and cyclic sieving is generalized to Möbius paths. We also discuss properties of a generalization of cyclic sieving, which we call subset cyclic sieving, and introduce the notion of Lyndon-like cyclic sieving that concerns special recursive properties of combinatorial objects exhibiting the cyclic sieving phenomenon. A corrigendum was added on November 6, 2020. An erratum was added on November 18, 2020.
@article{10_37236_8720,
author = {Per Alexandersson and Svante Linusson and Samu Potka},
title = {The cyclic sieving phenomenon on circular {Dyck} paths},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8720},
zbl = {1422.05006},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8720/}
}
TY - JOUR
AU - Per Alexandersson
AU - Svante Linusson
AU - Samu Potka
TI - The cyclic sieving phenomenon on circular Dyck paths
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8720/
DO - 10.37236/8720
ID - 10_37236_8720
ER -
%0 Journal Article
%A Per Alexandersson
%A Svante Linusson
%A Samu Potka
%T The cyclic sieving phenomenon on circular Dyck paths
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8720/
%R 10.37236/8720
%F 10_37236_8720
Per Alexandersson; Svante Linusson; Samu Potka. The cyclic sieving phenomenon on circular Dyck paths. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8720
