An asymptotic estimate of the numbers of rectangular drawings or floorplans
Ryo Fujimaki, Youhei Inoue · 2009
A subdivision of a rectangle into rectangular faces with horizontal and vertical line segments is called rectangular drawings or floorplans. It is known that the number of rectangular drawings R(n) is asymptotically approximated by a geometric progression, where n is the number of inner rectangles. More precisely, there exists a constant c = limn→∞R(n)1/n. The best upper and lower bounds of c ever known are 25 and 11.56, respectively. In this report, R(n) ≤ 13.5n−1is shown, which implies c ≤ 13.5.