A method for the enumeration of various classes of column-convex polygons

2 Abstract. We present a new method that allows to enumerate various classes of column-convex polygons, according to their perimeter and their area. The rst step of this method leads to a functional equation which deenes implicitly the generating function of the class under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual classes of column-convex polygons: thus, we rst reene some already known results for parallelogram polygons and for directed and convex polygons, and then obtain two new results, namely the generating function of column-convex polygons and of directed column-convex polygons.