Dimers and Spanning Trees

As we have seen, the set of dimer covers on a graph is in bijection with several other interesting objects. In this talk we will discuss a bijection between dimer covers on a graph and spanning trees on a related graph, a generalization of Temperley’s classic bijection. The powerful tools developed for spanning trees, like Wilson’s algorithm for selecting a uniformly random spanning tree can then be used on dimer covers as well.

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Date published: Wednesday, September 28, 2022