Counting $k$-Convex Polyominoes

Abstract

We compute an asymptotic estimate of a lower bound of the number of $k$-convex polyominoes of semiperimeter $p$. This approximation can be written as $\mu(k) p 4^p$ where $\mu(k)$ is a rational fraction of $k$ which up to $\mu(k)$ is the asymptotics of convex polyominoes.