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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 are pn SAPs of length n there are 2npn 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. |
Created: 24 April, 2000 Last modified: 24 April, 2000