A bijection between convex polyominoes and equations for their enumeration according to their area

A bijection between convex polyominoes and words of an algebraic language gives a system of q-equations for the generating function of these polyominoes according to their height, width and area. Enumerating convex polyominoes according to the area is an open problem. Although unable to solve these equations in the most general case, the results in this paper constitute a first step towards the solution.