We derive a decomposition scheme of unlabelled triangulations rooted at a single cell, where the decomposition depends on whether the automorphism group of the triangulation contains reflections, rotations, or both. Furthermore, the decomposition scheme is constructive in the sense that for each of the three cases, there is a $k\in\mathbb{N}$ such that the scheme defines a one-to-$k$ correspondence between the respective triangulations and their decompositions.
@article{10_37236_6188,
author = {Mihyun Kang and Philipp Spr\"ussel},
title = {Symmetries of unlabelled planar triangulations},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6188},
zbl = {1380.05037},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6188/}
}
TY - JOUR
AU - Mihyun Kang
AU - Philipp Sprüssel
TI - Symmetries of unlabelled planar triangulations
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6188/
DO - 10.37236/6188
ID - 10_37236_6188
ER -
%0 Journal Article
%A Mihyun Kang
%A Philipp Sprüssel
%T Symmetries of unlabelled planar triangulations
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6188/
%R 10.37236/6188
%F 10_37236_6188
Mihyun Kang; Philipp Sprüssel. Symmetries of unlabelled planar triangulations. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6188
