Gap Distributions in Circle Packings

TL;DR

This paper investigates the distribution of gaps between tangent points in specific circle packings, employing geometric methods and automorphic forms to analyze their spacing patterns.

Contribution

It introduces a novel approach combining geometry and automorphic forms to study gap distributions in circle packings generated by reflections.

Findings

Derived explicit gap distribution formulas

Identified statistical properties of tangent point spacings

Connected geometric configurations with automorphic form theory

Abstract

We determine the distribution of nearest neighbour spacings between the tangencies to a fixed circle in a class of circle packings generated by reflections. We use a combination of geometric tools and the theory of automorphic forms.