2-chains: an interesting family of posets

TL;DR

This paper introduces 2-chains, a new family of finite posets with multiple characterisations, originating from 0-Hecke algebra studies, and provides their properties and numerical results.

Contribution

The paper defines 2-chains, proves their equivalences across different characterisations, and explores their numerical properties.

Findings

Multiple characterisations of 2-chains established

Equivalence of different definitions proven

Numerical properties of 2-chains derived

Abstract

We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We give these characterisations, prove that they are equivalent and derive some numerical results concerning 2-chains.