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In this paper we present a bijection $\omega_n$ between two well knownfamilies of Catalan objects: the set of facets of the $m$-generalized clustercomplex $\Delta^m(A_n)$ and the set of dominant regions in the $m$-Catalanarrangement ${\rm Cat}^m(A_n)$, where $m\in\mathbb{N}_{>0}$. In particular,$\omega_n$ bijects the facets containing the negative simple root $-\alpha$ todominant regions having the hyperplane $\{v\in V\mid<v,\alpha >=m\}$ asseparating wall. As a result, $\omega_n$ restricts to a bijection between theset of facets of the positive part of $\Delta^m(A_n)$ and the set of boundeddominant regions in ${\rm Cat}^m(A_n)$. The map $\omega_n$ is a composition oftwo bijections in which integer partitions in an $m$-staircase shape come intoplay.

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