Cut Equivalence of d-Dimensional Guillotine Partitions

Andrei Asinowski, Gill Barequet, Toufik Mansour, Ron Y. Pinter

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A guillotine partition of a d-dimensional axis-aligned box B is a recursive partition of B by axis-aligned hyperplane cuts. Two guillotine partitions are box- equivalent if their boxes satisfy compatible order relations wrt. the axes. In this work we define cut-equivalence of guillotine partitions, derived in a similar way from order relations of cuts. We study structural properties of these kinds of equivalence, and enumerate cut-equivalence classes of d-dimensional guillotine partitions.

Original languageEnglish
Title of host publication29th European Workshop on Computational Geometry
Number of pages4
StatePublished - 2013

Bibliographical note

Funding Information:
Work on this paper by the first and second authors has been supported in part by a grant from Bar-Nir Bergreen Software Technology Center of Excellence .


  • Generating functions
  • Guillotine partitions
  • Inclusion-exclusion principle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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