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.
|Title of host publication||29th European Workshop on Computational Geometry|
|Number of pages||4|
|State||Published - 2013|
Bibliographical noteFunding 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