Conference Proceedings
Exact solution of two planar polygon models
AJ Guttmann, I Jensen
Nankai Tracts in Mathematics Differential Geometry and Physics Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics Dgmtp 2005 | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2006
Abstract
Using a simple transfer matrix approach we have derived long series expansions for the perimeter generating functions of both three-choice polygons and punctured staircase polygons. In both cases we find that all the known 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.
Grants
Funding Acknowledgements
We would like to thank N Zenine and J-M Maillard for access to their Mathematica routines and useful advice about their use. We would also like to thank M. Bousquet-Melou for communicating her unpublished results on this problem, which we mentioned in the introduction. We gratefully acknowledge financial support from the Australian Research Council.