A self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x, y) and partial generating functions H_m(y), connected by G(x, y, q) = sum_(m>=1) H_m(y, q) x^m, satisfy the self-reciprocity and inversion relations H_m(1/y, 1/q) = (-1)^m y^(m - 2) q^((m^3 - 3m)/2) H_m(y, q) and G(x, y) - y^2 G(-x/y, 1/y) = 0 .

lattice polygon | self-avoiding polygon