On the number of rectangulations of a planar point set

We investigate the number of different ways in which a rectangle containing a set of n noncorectilinear points can be partitioned into smaller rectangles by n (non-intersecting) segments, such that every point lies on a segment. We show that when the relative order of the points forms a separable permutation, the number of rectangulations is exactly the (n + 1)st Baxter number. We also show that no matter what the order of the points is, the number of guillotine rectangulations is always the nth Schr

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Eyal Ackerman, Gill Barequet, Ron Y. Pinter
• Keywords: JCT 2006, Noncorectilinear Points, Rectangles, Smaller Rectangles