Ordered partitions and drawings of rooted plane trees.

We study the bounded regions in a generic slice of the hyperplane arrangement in R n consisting of the hyperplanes defined by x i and x i + x j . 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. [ABSTRACT FROM AUTHOR]