Quasirandomness in additive groups and hypergraphs

TL;DR

This survey explores the concept of quasirandomness across graphs, hypergraphs, and additive groups, highlighting their interconnections and applications in understanding the properties of seemingly random combinatorial objects.

Contribution

It provides a comprehensive overview of quasirandomness in different mathematical structures and clarifies their relationships and uses in combinatorics.

Findings

Unified framework for quasirandomness across structures

Connections between graph, hypergraph, and additive group quasirandomness

Applications in studying properties of random-like combinatorial objects

Abstract

Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we explore this general concept as it applies to graphs, hypergraphs and additive groups, making clear their many connections to each other and showing how they can be used in order to better study these objects.