Home page of Dr Iwan Jensen
ARC Research Fellow Statistical Mechanics and Combinatorics Group Department of Mathematics and Statistics |

## Self-Avoiding PolygonsA self-avoiding polygon (SAP) can be defined as a walk on a lattice which returns to the origin and has no other self-intersections. Alternatively we can define a SAP as a connected sub-graph (of a lattice) whose vertices are of degree 2. Generally SAPs are considered distinct up to a translation, so if there arep SAPs of length _{n}n there are
2np walks (the factor of
two arising since the walk can go in two directions). The enumeration of
self-avoiding polygons on various lattices is an interesting combinatorial
problem in its own right, and is also of considerable importance in the
statistical mechanics of lattice models.
_{n} |

Created: 24 April, 2000 Last modified: 24 April, 2000