Authors: Christian Stump ¹; Hugh Thomas ²; Nathan Williams ²

• 1 Institute fur Mathematik
• 2 Laboratoire de combinatoire et d'informatique mathématique [Montréal]

The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations. We provide new viewpoints for these, introduce a corresponding generalization of sortable elements as elements in the positive Artin monoid, and show how this perspective ties together all three generalizations.