Facets of the $m$-generalized cluster complex and regions in the $m$-extended Catalan arrangement of type $A_n$

Susanna Fishel, Myrto Kallipoliti, Eleni Tzanaki

In this paper we present a bijection ${\omega }_n$ between two well known families of Catalan objects: the set of facets of the $m$-generalized cluster complex ${\Delta }^m(A_n)$ and the set of do…