Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.
Biane, Some properties of crossings and partitions , Discrete Math
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Fuss--Catalan algebras on generalized Dyck paths via non-crossing partitions
Fuss-Catalan algebras and their one- and two-boundary versions are realized on increasing chains of non-crossing partitions, with a new r=2 reflection equation solution.