English

Non-crossing partitions

Group Theory 2019-03-05 v1 Combinatorics Probability Representation Theory

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 non-crossing partitions are associated to Coxeter and Artin groups of type An\mathsf{A}_n, which explains the tight connection to the symmetric groups and braid groups. We shall outline those developments.

Keywords

Cite

@article{arxiv.1903.01146,
  title  = {Non-crossing partitions},
  author = {Barbara Baumeister and Kai-Uwe Bux and Friedrich Götze and Dawid Kielak and Henning Krause},
  journal= {arXiv preprint arXiv:1903.01146},
  year   = {2019}
}

Comments

Survey article, 34 pages, 7 figures

R2 v1 2026-06-23T07:57:15.356Z