On the Number of Rectangular Partitions

Eyal Ackerman, Gill Barequet, Ron Y. Pinter

Research output: Contribution to conferencePaperpeer-review


How many ways can a rectangle be partitioned into smaller ones? We study two variants of this problem: when the partitions are constrained to lie on n given points (no two of which are corectilinear), and when there are no such constraints and all we require is that the number of (non-intersecting) segments is n. In the first case, when the order (permutation) of the points conforms with a certain property, the number of partitions is the (n + 1)st Baxter number, B(n + 1); the number of permutations conforming with the property is the (n - 1)st Schröder number; and the number of guillotine partitions is the nth Schröder number. In the second case, it is known that the number of partitions and the number of guillotine partitions correspond to the Baxter and Schröder numbers, respectively. Our contribution is a bijection between permutations and partitions. Our results provide interesting and new geometric interpretations to both Baxter and Schröder numbers and suggest insights regarding the intricacies of the interrelations.

Original languageEnglish
Number of pages10
StatePublished - 2004
Externally publishedYes
EventProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States
Duration: 11 Jan 200413 Jan 2004


ConferenceProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew Orleans, LA.


  • Baxter permutations
  • Guillotine partitions
  • Quasimonotone permutations
  • Rectangular partitions
  • Schröder numbers

ASJC Scopus subject areas

  • Software
  • General Mathematics


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