Given a surface with boundary and some points on the boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on the surface. If only bigons are allowed, then one obtains the notion of arc diagrams, whose enumeration is known to have a rich structure. We show that the count of polygon diagrams on surfaces with any genus and number of boundary components exhibits similar structure. In particular it is almost polynomial in the number of points on the boundary components, and the leading coefficients of those polynomials are intersection numbers on compactified moduli spaces of curves.
@article{10_37236_9890,
author = {Norman Do and Jian He and Daniel V. Mathews},
title = {Counting non-crossing permutations on surfaces of any genus},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/9890},
zbl = {1476.05012},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9890/}
}
TY - JOUR
AU - Norman Do
AU - Jian He
AU - Daniel V. Mathews
TI - Counting non-crossing permutations on surfaces of any genus
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9890/
DO - 10.37236/9890
ID - 10_37236_9890
ER -
%0 Journal Article
%A Norman Do
%A Jian He
%A Daniel V. Mathews
%T Counting non-crossing permutations on surfaces of any genus
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9890/
%R 10.37236/9890
%F 10_37236_9890
Norman Do; Jian He; Daniel V. Mathews. Counting non-crossing permutations on surfaces of any genus. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/9890
