We study the relationship between rational slope Dyck paths and invariant subsets of $\mathbb{Z},$ extending the work of the first two authors in the relatively prime case. We also find a bijection between $(dn,dm)$–Dyck paths and $d$-tuples of $(n,m)$-Dyck paths endowed with certain gluing data. These are the first steps towards understanding the relationship between rational slope Catalan combinatorics and the geometry of affine Springer fibers and knot invariants in the non relatively prime case.
@article{10_37236_6901,
author = {Eugene Gorsky and Mikhail Mazin and Monica Vazirani},
title = {Rational {Dyck} paths in the non relatively prime case},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6901},
zbl = {1372.05017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6901/}
}
TY - JOUR
AU - Eugene Gorsky
AU - Mikhail Mazin
AU - Monica Vazirani
TI - Rational Dyck paths in the non relatively prime case
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6901/
DO - 10.37236/6901
ID - 10_37236_6901
ER -
%0 Journal Article
%A Eugene Gorsky
%A Mikhail Mazin
%A Monica Vazirani
%T Rational Dyck paths in the non relatively prime case
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6901/
%R 10.37236/6901
%F 10_37236_6901
Eugene Gorsky; Mikhail Mazin; Monica Vazirani. Rational Dyck paths in the non relatively prime case. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6901
