A probabilistic proof of a lemma that is not Burnside's

TL;DR

This paper presents a probabilistic proof of the orbit-counting lemma, offering an alternative approach to a fundamental combinatorial result in group actions.

Contribution

It introduces a novel probabilistic method to prove the orbit-counting lemma, expanding the toolkit for combinatorial and group theory proofs.

Findings

Probabilistic proof of the orbit-counting lemma

Alternative approach to classical combinatorial proofs

Potential applications in group action analysis

Abstract

We give a probabilistic proof of the orbit-counting lemma.