On Noncrossing and nonnesting partitions of type D

TL;DR

This paper introduces an explicit bijection between noncrossing and nonnesting partitions of Coxeter systems of type D, preserving key structural elements.

Contribution

It provides a novel explicit bijection for type D Coxeter systems that maintains openers, closers, and transients, advancing combinatorial understanding.

Findings

Bijection preserves key partition features

Enhances combinatorial theory of Coxeter groups

Bridges noncrossing and nonnesting partitions in type D

Abstract

We present an explicit bijection between noncrossing and nonnesting partitions of Coxeter systems of type D which preserves openers, closers and transients.