Article

On the number of rectangular partitions

Authors:

Ron Y. PinterAuthors Info & Claims

SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

Pages 736 - 745

Published: 11 January 2004 Publication History

Abstract

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 [22] 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.

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Cited By

Ackerman EBarequet GPinter R(2005)An Upper Bound on the Number of Rectangulations of a Point SetProceedings of the 11th Annual International Conference on Computing and Combinatorics - Volume 359510.5555/2958119.2958137(554-559)Online publication date: 16-Aug-2005
https://dl.acm.org/doi/10.5555/2958119.2958137

On the number of rectangular partitions
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
2. Theory of computation

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cover image ACM Conferences

SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

January 2004

1113 pages

ISBN:089871558X

Program Chair:
Ian Munro

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

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Published: 11 January 2004

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Cited By

Ackerman EBarequet GPinter R(2005)An Upper Bound on the Number of Rectangulations of a Point SetProceedings of the 11th Annual International Conference on Computing and Combinatorics - Volume 359510.5555/2958119.2958137(554-559)Online publication date: 16-Aug-2005
https://dl.acm.org/doi/10.5555/2958119.2958137

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