We prove that every set of n points in the plane has at most $(16+\frac{5}{6})^n$ rectangulations. This improves upon a long-standing bound of Ackerman. Our proof is based on the cross-graph charging-scheme technique.
@article{10_37236_11398,
author = {Hannah Ashbach and Kiki Pichini},
title = {An upper bound for the number of rectangulations of a planar point set},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/11398},
zbl = {1546.52021},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11398/}
}
TY - JOUR
AU - Hannah Ashbach
AU - Kiki Pichini
TI - An upper bound for the number of rectangulations of a planar point set
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/11398/
DO - 10.37236/11398
ID - 10_37236_11398
ER -
%0 Journal Article
%A Hannah Ashbach
%A Kiki Pichini
%T An upper bound for the number of rectangulations of a planar point set
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11398/
%R 10.37236/11398
%F 10_37236_11398
Hannah Ashbach; Kiki Pichini. An upper bound for the number of rectangulations of a planar point set. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11398
