Ordered partitions and drawings of rooted plane trees

We study the bounded regions in a generic slice of the hyperplane arrangement in Rn consisting of the hyperplanes defined by xi and xi+xj. The bounded regions are in bijection with several classes of combinatorial objects, including the ordered partitions of [n] all of whose left-to-right minima occur at odd locations and the drawings of rooted plane trees with n+1 vertices. These are sequences of rooted plane trees such that each tree in a sequence can be obtained from the next one by removing a leaf.