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 , which explains the tight connection to the symmetric groups and braid groups. We shall outline those developments.
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