# Kasteleyn cokernels and perfect matchings on planar bipartite graphs

@article{Taylor2018KasteleynCA, title={Kasteleyn cokernels and perfect matchings on planar bipartite graphs}, author={Libby Taylor}, journal={arXiv: Combinatorics}, year={2018} }

The determinant method of Kasteleyn gives a method of computing the number of perfect matchings of a planar bipartite graph. In addition, results of Bernardi exhibit a bijection between spanning trees of a planar bipartite graph and elements of its Jacobian. In this paper, we explore an analogue of Bernardi's results, providing a canonical simply transitive group action of the Kasteleyn cokernel of a planar bipartite graph on its set of perfect matchings, when the planar bipartite graph in… Expand

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