Regions of the type C Catalan arrangement

Abstract

In this paper, we give a bijection between rooted labeled ordered forests with a selected subset of their leaves and the regions of the type $C$ Catalan arrangement in ${\mathbb{R}}^n$. We thus obtain a bijective proof of the well-known enumeration formula of these regions $2^{n}n!\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$.

10 pages, 3 figures