Chris Soteros - University of Saskatchewan
Asymptotic properties of the number of lattice embeddings of a graph
One question that has captured the interest of lattice model researchers since at least the 1970's is: how does the asymptotic form of the number of embeddings of a graph in the d-dimensional hypercubic lattice depend on the properties of the graph? In 1978 Guttmann and Whittington addressed this question for the case of figure eight, dumbell and theta graphs in the square lattice and proved, for example, that the exponential growth rate of the number of dumbells or theta graphs is the same as that for self-avoiding walks, i.e. independent of the graph type. In this talk I will review some of the progress that has been made since then towards answering the general question above. The focus will be on what has been proved using combinatorial arguments and bounds.