• 1 Dipartimento di Sistemi e Informatica
• 2 Department of Mathematics and Computer Science / Dipartimento di Scienze Matematiche e Informatiche "Roberto Magari"

In this paper we consider the class of $\textit{permutominoes}$, i.e. a special class of polyominoes which are determined by a pair of permutations having the same size. We give a characterization of the permutations associated with convex permutominoes, and then we enumerate various classes of convex permutominoes, including parallelogram, directed-convex, and stack ones.