Laver tables and combinatorics

TL;DR

This paper introduces Laver tables, finite combinatorial objects from logic and set theory, highlighting their properties and open problems to engage the combinatorics community.

Contribution

It provides the first accessible introduction to Laver tables, detailing their definition, properties, and open problems, bridging logic and combinatorics.

Findings

Laver tables have unique combinatorial properties.

They connect logic, set theory, and combinatorics.

Open problems suggest further research directions.

Abstract

The Laver tables are finite combinatorial objects with a simple elementary definition, which were introduced by R. Laver from considerations of logic and set theory. Although these objects exhibit some fascinating properties, they seem to have escaped notice from the combinatorics community. My aim is to give a short introduction to this topic, presenting the definition and main properties and stating a few open problems, which should arouse the interest of combinatorialists.