The number of guillotine partitions in d dimensions

Authors:
Eyal Ackerman;Gill Barequet;Ron Y. Pinter;Dan Romik
Affiliations:
Department of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel;Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel
Venue:
Information Processing Letters
Year:
2006

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Abstract

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 Θ((2d- 1 + 2√d(d-1))n/n3/2).