Permutations defining convex permutominoes

Abstract

A permutomino of size n is a polyomino determined by particular pairs (π 1 , π 2 ) of permutations of size n, such that πHere we determine the combinatorial properties and, in particular, the characterization for the permutations defining convex permutominoes.Using such a characterization, these permutations can be uniquely represented in terms of the so called square permutations, introduced by Mansour and Severini. Then, we provide a closed formula for the number of these permutations with size n.