Exact solution of the row-convex polygon perimeter generating function

Abstract

An explicit expression is obtained for the perimeter generating function G(y)= Sigma n>or=2 any2n for row-convex polygons on the square lattice, where an is the number of 2n step row-convex polygons. An asymptotic expression for an approximately A mu nn-3/2 is obtained, where mu =3+22 and A are given. The authors also show that the generating function is an algebraic function and that it satisfies an inhomogeneous linear differential equation of degree three.