L-Convex Polyominoes: Geometrical Aspects

A polyomino P is called L-convex if for every two cells there exists a monotone path included in P with at most one change of direction. This paper is a theoretical step for the reconstruction of all L-convex polyominoes by using the geometrical paths. First we investigate the geometrical properties of all subclasses of non-directed L-convex polyominoes by giving nine geometries that characterize all non-directed L-convex polyominoes. Finally, we study the subclasses of directed L-convex polyominoes and we give necessary and sufficient conditions for polyominoes to be L-convex.