On maximal chains in the non-crossing partition lattice

TL;DR

This paper introduces a weak order on maximal chains in the non-crossing partition lattice and uses a 0-Hecke algebra action to analyze the graph structure of these chains, revealing new combinatorial insights.

Contribution

It presents a novel weak order on maximal chains and applies algebraic methods to study the adjacency graph of these chains, advancing understanding of their combinatorial properties.

Findings

Defined a weak order on maximal chains in the non-crossing partition lattice

Used 0-Hecke algebra action to compute the graph radius of chain adjacency

Provided new combinatorial and algebraic insights into the structure of these chains

Abstract

A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ in exactly one element.