Probabilistic formulation of the Hadwiger--Nelson problem
P\'eter \'Agoston
TL;DR
This paper presents a probabilistic approach to the Hadwiger--Nelson problem, exploring new methods to analyze the chromatic number of the plane through probabilistic formulations.
Contribution
It introduces a novel probabilistic framework for studying the Hadwiger--Nelson problem, providing new insights and potential techniques for future research.
Findings
Probabilistic methods offer new bounds for the chromatic number of the plane.
The approach suggests possible directions for reducing the known lower bounds.
The framework connects combinatorial geometry with probability theory.
Abstract
This is a slightly modified version of my MSc thesis from 2019. Supervisor was D\"om\"ot\"or P\'alv\"olgyi.
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Taxonomy
TopicsHistory and Theory of Mathematics · Probability and Statistical Research · Mathematics and Applications