The number of guillotine partitions in d dimensions

Guillotine partitions play an important role in many research areas and application domains, e.g., computational geometry, computer graphics, integrated circuit layout, and solid modeling, to mention just a few. In this paper we present an exact summation formula for the number of structurally-different guillotine partitions in d dimensions by n hyperplanes, and then show that it is 2d - 1 + 2 d(d - 1) n /n3/2 .

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: Eyal Ackerman, Gill Barequet, Ron Y. Pinter, Dan Romik
• Keywords: Exact Summation Formula, Guillotine Partitions, Integrated Circuit Layout, IPL 2006