Exact solution of the row-convex polygon perimeter generating function
- 21 June 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (12) , 2319-2326
- https://doi.org/10.1088/0305-4470/23/12/016
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.Keywords
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