PERIMETER AND AREA GENERATING-FUNCTIONS OF THE STAIRCASE AND ROW-CONVEX POLYGONS ON THE RECTANGULAR LATTICE

The two-variable perimeter and area generating functions derived recently by Brak and Guttmann for the staircase and row-convex polygons on the square lattice are generalized to the rectangular lattice. We consider the three-variable generating function [GRAPHICS] is the number of appropriate polygons with 2n horizontal steps, 2m vertical steps and area r. Two generating functions G(x, y, z) for the staircase and row-convex polygons are derived. We also calculate the generating functions for the first and second area-weighted moments by the perturbation method of Lin.