Andrea Frosini

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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)
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)
ECO is a method for the recursive generation, and thereby also the enumeration of classes of combinatorial objects. It has already found successful application in recent literature both to the exhaustive generation and to the uniform random generation of various objects classified according to several parameters of interest, as well as to their enumeration.(More)
A binary matrix can be scanned by moving a fixed rectangular window (sub-matrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of(More)