"The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuss-Catalan generalizations. We provide new viewpoints for both and introduce the missing generalization of sortable elements by lifting the theory from the Coxeter system to the associated positive Artin monoid. We show how this new perspective ties together all three generalizations, providing a uniform framework for noncrossing Fuss-Catalan combinatorics. Having developed the combinatorial theory, we provide an interpretation of our generalizations in the language of the representation theory of hereditary Artin algebras"-- Provided by publisher.
1. Introduction
2. Background on Coxeter and Artin groups
3. Subword complexes
4. Noncrossing partitions
5. Cluster complexes
6. Sortable elements
7. Positive $m$-eralized structures
8. Conjectures on rational structures
9. $m$-eralized structures in representation theory
Christian Stump, Ruhr-Universitat Bochum, Germany.
Hugh Thomas, Universite du Quebec a Montreal, Quebec, Canada.
Nathan Williams, University of Texas at Dallas, Texas.
