@Article{KR74, author = { David A. Klarner and Ronald L. Rivest }, title = { Asymptotic Bounds for the Number of Convex $n$-ominoes }, journal = { Discrete Mathematics }, OPTyear = { 1974 }, OPTmonth = { March }, date = { 1974-03 }, volume = { 8 }, number = { 1 }, pages = { 31--40 }, doi = { 10.1016/0012-365X(74)90107-1 }, url = { http://www.sciencedirect.com/science/article/pii/0012365X74901071 }, abstract = { Unit squares having their vertices at integer points in the Cartesian plane are called cells. A point set equal to a union of $n$ distinct cells which is connected and has no finite cut set is called an $n$-omino. Two $n$-ominoes are considered the same if one is mapped onto the other by some translation of the plane. An $n$-omino is convex if all cells in a row or column form a connected strip. Letting $c(n)$ denote the number of different convex $n$-ominoes, we show that the sequence $((c(n))^{1/n}: n=1,2,\ldots)$ tends to a limit $\gamma$ and $\gamma=2.309138\ldots .$ }, }