On the number of rectangular partitions

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 Schr

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Eyal Ackerman, Gill Barequet, Ron Y. Pinter
• Keywords: Algorithms, Baxter Number, Guillotine Partitions, Schr¨oder Numbers, SODA 2004