Abstract
A composite polygon is composed of a lattice polygon in the square lattice, which contains in its interior an internal structure, which may also be a lattice polygon, or a lattice tree or a lattice animal, or a lattice disc (or a collection of these). The properties of composite polygons are considered in this manuscript. In particular, I shall consider the growth constants and generating functions of these models, as well as the statistical mechanics of interacting models of composite polygons. It is shown that there is an adsorption transition of the internal structure on the containing polygon, and a transition which corresponds to the inflation of the containing polygon (by the internal structure).
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