# Non-crossing partitions

• ### Barbara Baumeister

Universität Bielefeld, Germany
• ### Kai-Uwe Bux

Universität Bielefeld, Germany
• ### Friedrich Götze

Universität Bielefeld, Germany
• ### Dawid Kielak

Universität Bielefeld, Germany
• ### Henning Krause

Universität Bielefeld, Germany

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## Abstract

Non-crossing partitions have been a staple in combinatorics for quite some time. More recently, they have surfaced (sometimes unexpectedly) in various other contexts from free probability to classifying spaces of braid groups. Also, analogues of the non-crossing partition lattice have been introduced. Here, the classical noncrossing partitions are associated to Coxeter and Artin groups of type A$_n$, which explains the tight connection to the symmetric groups and braid groups. We shall outline those developments.