On the number of rectangulations of a planar point set

Eyal Ackerman; Gill Barequet; Ron Y. Pinter

doi:10.1016/j.jcta.2005.10.003

On the number of rectangulations of a planar point set

Eyal Ackerman, Gill Barequet, Ron Y. Pinter

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1072-1091
Number of pages	20
Journal	Journal of Combinatorial Theory. Series A
Volume	113
Issue number	6
DOIs	https://doi.org/10.1016/j.jcta.2005.10.003
State	Published - Aug 2006
Externally published	Yes

Keywords

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

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10.1016/j.jcta.2005.10.003

Cite this

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title = "On the number of rectangulations of a planar point set",

abstract = "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 Schr{\"o}der number, and the total number of rectangulations is O (20n / n4).",

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AU - Barequet, Gill

AU - Pinter, Ron Y.

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N2 - 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).

AB - 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).

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KW - Guillotine partitions

KW - Rectangular partitions

KW - Rectangulations

KW - Schröder numbers

KW - Separable permutations

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On the number of rectangulations of a planar point set

Abstract

Keywords

ASJC Scopus subject areas

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