Cataland: Why the Fuss?

Christian Stump (1) , Hugh Thomas (2) , Nathan Williams (2)

1 Institute fur Mathematik
2 LaCIM - 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.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Christian Stump, Hugh Thomas, Nathan Williams. Cataland: Why the Fuss?. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6351⟩. ⟨hal-02166329⟩