On the number of rectangulations of a planar point set

Eyal Ackerman, Gill Barequet, Ron Y. Pinter

Research output: Contribution to journalArticlepeer-review


We investigate the number of different ways in which a rectangle containing a set of n noncorectilinear points can be partitioned into smaller rectangles by n (nonintersecting) segments, such that every point lies on a segment. We show that when the relative order of the points forms a separable permutation, the number of rectangulations is exactly the (n + 1)st Baxter number. We also show that no matter what the order of the points is, the number of guillotine rectangulations is always the nth Schröder number, and the total number of rectangulations is O (20n / n4).

Original languageEnglish
Pages (from-to)1072-1091
Number of pages20
JournalJournal of Combinatorial Theory. Series A
Issue number6
StatePublished - Aug 2006
Externally publishedYes


  • Baxter permutations
  • Guillotine partitions
  • Rectangular partitions
  • Rectangulations
  • Schröder numbers
  • Separable permutations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


Dive into the research topics of 'On the number of rectangulations of a planar point set'. Together they form a unique fingerprint.

Cite this