An Upper Bound for the Number of Rectangulations of a Planar Point Set

TL;DR

This paper establishes a new upper bound on the number of rectangulations for any set of n points in the plane, improving previous bounds using a novel proof technique.

Contribution

It introduces a tighter upper bound for rectangulations of planar point sets and employs a cross-graph charging-scheme method.

Findings

Proves an upper bound of (16+5/6)^n for rectangulations.

Improves upon Ackerman's previous bound.

Uses a novel proof technique based on cross-graph charging-scheme.

Abstract

We prove that every set of n points in the plane has at most $(16+5/6)^n$ rectangulations. This improves upon a long-standing bound of Ackerman. Our proof is based on the cross-graph charging-scheme technique.