Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Cataland: Why the Fuss?
Christian Stump  1  , Hugh Thomas  2  , Nathan Williams  2  
1 : Institute für Mathematik, Freie Universität Berlin, Germany
2 : Laboratoire de combinatoire et d'Informatique mathématique [Montréal]  (LaCIM)  -  Website
LaCIM Pavillon Président-Kennedy 201 CP 8888, Succ. Centre-ville Montréal (Québec) H3C 3P8 -  Canada

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. 

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