A Statistical Approach to Broken Stick Problems

TL;DR

This paper introduces a statistical method using linear transformations to efficiently solve problems related to forming polygons from randomly broken stick segments.

Contribution

It presents a novel statistical approach that simplifies and accelerates solutions to broken stick problems involving polygon formation.

Findings

Provides simple solutions for k-gon formation problems

Enables fast computation of probabilities and configurations

Introduces a linear transformation technique for analysis

Abstract

Let a stick be broken at random at n-1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, and show how a statistical approach, through a linear transformation of variables, yields simple solutions that also allow fast computation.