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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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