Rigorous results for the number of convex polygons on the square and honeycomb lattices
- 7 June 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (11) , 2635-2642
- https://doi.org/10.1088/0305-4470/21/11/020
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.Keywords
This publication has 3 references indexed in Scilit:
- The number of convex polygons on the square and honeycomb latticesJournal of Physics A: General Physics, 1988
- The size and number of rings on the square latticeJournal of Physics A: General Physics, 1988
- Number of anisotropic spiral self-avoiding loopsJournal of Physics A: General Physics, 1987