Exact solution of the row-convex polygon perimeter generating function

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, , Citation R Brak et al 1990 J. Phys. A: Math. Gen. 23 2319 DOI 10.1088/0305-4470/23/12/016

0305-4470/23/12/2319

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.

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10.1088/0305-4470/23/12/016