Non-crossing partitions
The systematic study of noncrossing partitions goes back to G. Kreweras in the 1970s where he considered set partitions on {1,...,n} with noncrossing blocks when drawn on a circle [Kre]. Among other beautiful properties, such noncrossing set partitions are counted by the famous Catalan numbers and they form a lattice under the refinement order.
More than 30 years later, D. Bessis and, independently, T. Brady and C. Watt provided an algebraic framework to generalize noncrossing partitions to finite Coxeter groups in a very natural and beautiful way [Bes03, BW02]. These developments opened the new combinatorial field of "Coxeter-Catalan combinatorics", see [Arm06] for further background and references. The final link to representations of quivers arose shortly after from the connection between noncrossing partitions and cluster algebras [Rea08] and their categorification via cluster categories [IT09].
This workshop is devoted to all aspects of this exciting development with the objective to bring together specialists interested in noncrossing partitions, in particular those from algebraic combinatorics and from quiver representation theory.
| [Arm06] | , Generalized noncrossing partitions and combinatorics of Coxeter groups, Mem. Amer. Math. Soc. 202 (2006). |
| [Bes03] | , The dual braid monoid, Ann. Sci. Ecole Norm. Sup. 36 (2003). |
| [BW02] | and , K(π,1)'s for Artin groups of finite type, Geom. Dedicata 94 (2002). |
| [IT09] | and , Noncrossing partitions and representations of quivers, Compositio Math. 145 (2009). |
| [Rea08] | , Clusters, Coxeter-sortable elements and noncrossing partitions, Trans. Amer. Math. Soc. 359 (2007). |
| [Kre72] | , Sur les partitions non croisées d'un cycle, Discrete Math. 1 (1972). |