Ordered partitions and drawings of rooted plane trees

摘要

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. (C) 2014 Elsevier B.V. All rights reserved.