A tiling system for the class of L-convex polyominoes

A polyomino is said to be L-convex if any two of its cells can be connected by a path entirely contained in the polyomino, and having at most one change of direction. In this paper, answering a problem posed by Castiglione and Vaglica, we prove that the class of L-convex polyominoes is tiling recognizable. To reach this goal, first we express the L-convexity constraint in terms of a set of independent properties, then we show that each class of convex polyominoes having one of these properties is tiling recognizable.