Fast heuristics for minimum length rectangular partitions of polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Enumerative combinatorics
Improved bounds for rectangular and guillotine partitions
Journal of Symbolic Computation
Bootstrap percolation, the Schro¨der numbers, and the N-kings problem
SIAM Journal on Discrete Mathematics
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Proceedings of the 7th conference on Formal power series and algebraic combinatorics
Bounds for partitioning rectilinear polygons
SCG '85 Proceedings of the first annual symposium on Computational geometry
Revisiting floorplan representations
Proceedings of the 2001 international symposium on Physical design
Corner block list: an effective and efficient topological representation of non-slicing floorplan
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Floorplan representations: Complexity and connections
ACM Transactions on Design Automation of Electronic Systems (TODAES)
The “PI” (placement and interconnect) system
DAC '82 Proceedings of the 19th Design Automation Conference
A bijection between permutations and floorplans, and its applications
Discrete Applied Mathematics
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
An upper bound on the number of rectangulations of a point set
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
| Hi-index | 0.00 |
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.