Enumerazione di poliomini che pavimentano il piano

Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those 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 = XYXY. We consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of psp-polyominoes with a fixed planar basis according to the semi-perimeter. The case of pseudo-square convex polyominoes is also analyzed.