Abstract
We consider the generating function of self-avoiding square lattice polygons grouped by both area and perimeter. The generating function for polygons of arean is found to diverge atx c =0.251834, with an exponent of zero. The mean perimeter of polygons with arean is found to be proportional ton, while the mean area of polygons with perimetern is found to be proportional ton 1.5.
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Enting, I.G., Guttmann, A.J. On the area of square lattice polygons. J Stat Phys 58, 475–484 (1990). https://doi.org/10.1007/BF01112757
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DOI: https://doi.org/10.1007/BF01112757