Self-avoiding polygons — towards an exact solution?

Abstract

We argue by analogy with other exactly solved models that the self-avoiding polygon problem is likely to be simpler than the self-avoiding walk problem. By greatly extending the series expansions for the square lattice polygon generating function, we obtain very precise numerical information, as well as good evidence for a particular underlying functional form. The exact solution of the (simpler) convex polygon problem is obtained, and current work on the hexagonal lattice polygon problem is described.