Journal article

Some solvable, and as yet unsolvable, polygon and walk models

Anthony J Guttmann, J DeGier (ed.), O Warnaar (ed.)

International Workshop on Statistical Mechanics and Combinatorics: Counting Complexity | IOP PUBLISHING LTD | Published : 2006

Abstract

One partly solvable and two solvable models of polygons are discussed. Using a simple transfer matrix approach Iwan Jensen has derived very long series expansions for the perimeter generating function of both three-choice polygons and punctured staircase polygons. In both cases it is found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We report on an analysis of the properties of the differential equations. Recently Enrica Duchi has discussed the problem of so-called prudent self-avoiding walks. We discuss the polygon analogue of this problem, and argue that the generating function for prudent polygons is unlikely to ..

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University of Melbourne Researchers