# Exact solution of two classes of prudent polygons

*Statistical Mechanics/Combinatorics Seminar*

*by Uwe Schwerdtfeger*

*Institution:*University of Bielefeld

*Date: Mon 28th July 2008*

*Time: 1:00 PM*

*Location: Old Geology Theatre 2, The University of Melbourne*

*Abstract*: A prudent walk is a walk on the square lattice consisting of

nearest neighbour steps, such that in the course the walker never steps

towards an occupied vertex, no matter at what distance. In particular,

such a walk is self-avoiding.

Three subclasses of such walks, called one-, two- and three-sided

prudent walks, have been solved so far. The first class has a rational

generating function. The second was shown to have an algebraic

generating function by E. Ducci in 2005. Recently, Mireille

Bousquet-Melou solved these two classes and the third, whose

generating function turns out to be non-holonomic.

In this talk we study polygon versions of the two- and three-sided

walks, meaning walks ending at a vertex adjacent to their starting

point. Similar to the walk cases, we find an algebraic generating

function for the former and a non-holonomic one for the latter class.

*For More Information:* Contact: Iwan Jensen I.Jensen@ms.unimelb.edu.au