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In this paper we determine a closed formula for the number of convex permu-tominoes 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(More)
In this paper we consider the class of 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(More)
A permutomino of size n is a polyomino whose vertices define a pair of distinct permutations of length n. In this paper we treat various classes of convex permutominoes, including the parallelogram, the directed convex and the stack ones. Using bijective techniques we provide enumeration for each of these classes according to the size, and characterize the(More)
Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word W may be factorized as W = XY X Y. In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using(More)
We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an " L " shaped path in one of its four cyclic orientations. The paper proves bijectively that the number f n of L-convex polyominoes with perimeter 2(n + 2) satisfies the linear recurrence relation f n+2 = 4 f n+1 − 2 f n , by first(More)
In this paper we introduce a new class of binary matrices whose entries show periodical configurations, and we furnish a first approach to their analysis from a tomographical point of view. In particular we propose a polynomial-time algorithm for reconstructing matrices with a special periodical behavior from their horizontal and vertical projections. We(More)