A View From The Bridge Spanning Combinatorics and Probability

TL;DR

This paper explores the deep connections between combinatorics and probability, providing accessible explanations and proofs aimed at combinatorialists to enhance understanding of their interplay.

Contribution

It offers a comprehensive overview of combinatorics-probability links with complete or well-developed proofs, tailored for combinatorialists.

Findings

Illustrates fundamental concepts bridging combinatorics and probability

Provides accessible proofs and explanations for key results

Highlights the relevance of probabilistic methods in combinatorial problems

Abstract

This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author's own interests, tastes and familiarity, as well as by a desire to present results with either complete proofs or well developed sketches of proofs, and to ensure that the arguments are rather accessible to combinatorialists. The first several sections collect some concepts and rudimentary results from probability theory that are needed to understand the rest of the paper.