Séminaire Lotharingien de Combinatoire, B54c (2005), 14 pp.

Anthony J. Guttmann and Iwan Jensen

Fuchsian Differential Equation for the Perimeter Generating Function of Three-Choice Polygons

Abstract. Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of three-choice polygons. We find that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We perform an analysis of the properties of the differential equation.

Received: June 10, 2005. Accepted: August 29, 2005. Final Version: September 15, 2005.

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