Exact solution for a model of punctured staircase polygons
by Dr Iwan Jensen
Abstract: We present the exact solution for the problem of a staircase polygon with a rotated
internal staircase polygon. A while ago we enumerated the exact number of such polygons. Using this series we found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation. We managed to solve the ODE and find a closed form expression for the generating function. We have since been able to prove this results exactly using combinatorial
arguments. This solution allows a generalisation to a model with any fixed number of nested punctures as well as to other types of polygons.
This is joint work with Andrew Rechnitzer and Mike Zabrocki.
For More Information: Dr. Iwan Jensen Phone: +61 3 8344 5214 I.Jensen@ms.unimelb.edu.au