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Number of almost-convex polygons on the square lattice

K Y Lin

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The generating function for the number Nc,n of almost-convex polygons on the square lattice with concavity index c=1 and perimeter n is derived rigorously. The asymptotic behaviour of Nc,n for large n is determined and this result confirms a conjecture by Enting et al. (1992).


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

02.40.-k Geometry, differential geometry, and topology

MSC

51E12 Generalized quadrangles, generalized polygons

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 7 (7 April 1992)



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