Abstract
The generating functions for the number of convex polygons on the square and honeycomb lattices are derived rigorously. These functions were found by Guttmann and Enting (1988). Their calculation is based on the series expansions up to the 64th order and is nonrigorous. The asymptotic form of the mean-squared radius of gyration of n-step convex polygons on the square lattice is determined and the critical exponent v is 1.
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