Tony Guttmann - The University of Melbourne
Some solvable and as yet unsolvable polygon and walk models
Recently, in joint work with Iwan Jensen, two polygon models have been found to satisfy high-order Fuchsian differential equations. They are polygon three-choice polygons and punctured staircase polygons. I will describe the solution process and singularity structure of the solutions.
A recently introduced, and currently unsolved, variant of self-avoiding walks, called prudent self-avoiding walks will be discussed, and shown not to be D-finite. However a series of recursions gives a polynomial-time algorithm for their generation, which suggests that they masy be easier to solve than ordinary SAW.