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 | |
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