On The Number Of Convex Polyominoes

. Lin and Chang gave a generating function for the number of convex polyominoes with an m+1byn+ 1 minimal bounding rectangle. We show that their result implies that the number of such polyominoes is m+ n +mn m+ n # 2m +2n 2m # - 2(m + n) # m+ n - 1 m ## m+ n - 1 n # . Resum e. Lin et Chang ont donnelaserie generatrice du nombre de polyominos convexes qui s'inscrivent dans un rectangle minimal de format m + 1 par n + 1. Nous montrons que ce resultat entrane que le nombre de tels polyominos est egal a m+ n +mn m+ n # 2m +2n 2m # - 2(m + n) # m+ n - 1 m ## m+ n - 1 n # . A polyomino is a connected union of squares in the plane whose vertices are lattice points. A polyomino is called convex if its intersection with any horizontal or vertical line is either empty or a line segment. (Note that a convex polyomino is generally not a convex polygon in the usual sense.) Any convex polyomino has a minimal bounding rectangle whose perimeter is the same as tha..