On the distribution of monochromatic complete subgraphs and arithmetic progressions

TL;DR

This paper studies how monochromatic complete subgraphs and arithmetic progressions are distributed in 2-colorings, providing evidence that these distributions are well-approximated by the Delaporte distribution, advancing statistical Ramsey theory.

Contribution

It introduces the use of the Delaporte distribution to model the distributions of monochromatic structures in 2-colorings, offering new insights into their probabilistic behavior.

Findings

Distributions are well-approximated by the Delaporte distribution.

Provides statistical evidence supporting the approximation.

Enhances understanding of Ramsey theory through probabilistic modeling.

Abstract

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.