Let $a < b$ be coprime positive integers. Armstrong, Rhoades, and Williams (2013) defined a set NC(a,b) of `rational noncrossing partitions', which form a subset of the ordinary noncrossing partitions of $\{1, 2, \dots, b-1\}$. Confirming a conjecture of Armstrong et. al., we prove that NC(a,b) is closed under rotation and prove an instance of the cyclic sieving phenomenon for this rotational action. We also define a rational generalization of the $\mathfrak{S}_a$-noncrossing parking functions of Armstrong, Reiner, and Rhoades.
@article{10_37236_5681,
author = {Michelle Bodnar and Brendon Rhoades},
title = {Cyclic sieving and rational {Catalan} theory},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5681},
zbl = {1335.05020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5681/}
}
TY - JOUR
AU - Michelle Bodnar
AU - Brendon Rhoades
TI - Cyclic sieving and rational Catalan theory
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5681/
DO - 10.37236/5681
ID - 10_37236_5681
ER -
%0 Journal Article
%A Michelle Bodnar
%A Brendon Rhoades
%T Cyclic sieving and rational Catalan theory
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5681/
%R 10.37236/5681
%F 10_37236_5681
Michelle Bodnar; Brendon Rhoades. Cyclic sieving and rational Catalan theory. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5681
