A combinatorial method for the enumeration of column-convex polyominoes Original Research Article

A new generating function enumerating column-convex polyominoes is defined and determined. The expression of the generating function which enumerates polyominoes according to area and number of columns, obtained by Delest (1988), immediately follows as a particular case. Our method is constructive and clearly explains the rational nature of these functions. In the last part, another enumerative application of this method is also presented.