A polyomino is a planar connguration consisting of some nite number of squares connected edge-to-edge. There is a large body of literature concerning polyominoes, much of it in the pages of this journal. A standard reference work is the book by Golomb 1]. Recently, while searching for a copy of the puzzle based on the twelve pentominoes, I came across a related puzzle called the \IQ-block". Thi...

A permutomino of size n is a polyomino determined by a pair (π1, π2) of permutations of size n + 1, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n+ 1. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the exhaustive generation of a particular class of permutominoes, the convex permutominoes, proving that its cost is proportional to the number of...

We give aO(n)-time algorithm for determining whether translations of a polyomino with n edges can tile the plane. The algorithm is also a O(n)-time algorithm for enumerating all regular tilings, and we prove that at most Θ(n) such tilings exist.

We present an algorithm to compute the degree of convexity of a convex polyomino P , defined as the smallest integer k such that any two cells of P can be joined by a path in P with at most k changes of direction. The algorithm is used to generate in amortized time O(1) all k-convex polyominoes of size n.

In this paper we determine a closed formula for the number of convex permutominoes of size n. We reach this goal by providing a recursive generation of all convex permutominoes of size n+1 from the objects of size n, according to the ECO method, and then translating this construction into a system of functional equations satisfied by the generating function of convex permutominoes. As a consequ...