The number of guillotine partitions in d dimensions

Eyal Ackerman, Gill Barequet, Ron Y. Pinter, Dan Romik

Research output: Contribution to journalArticlepeer-review


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+2d(d-1))n/n3/2).

Original languageEnglish
Pages (from-to)162-167
Number of pages6
JournalInformation Processing Letters
Issue number4
StatePublished - 31 May 2006
Externally publishedYes

Bibliographical note

Funding Information:
✩ Work on this paper by the first and second authors has been supported in part by AIM@SHAPE, a grant of the European Commission 6th Framework. * Corresponding author. E-mail addresses: (E. Ackerman), (G. Barequet), (R.Y. Pinter), (D. Romik).


  • Binary space partitions
  • Combinatorial problems
  • Guillotine partitions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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