# A Pfaffian Formula for Monomer–Dimer Partition Functions

@article{Giuliani2015APF, title={A Pfaffian Formula for Monomer–Dimer Partition Functions}, author={Alessandro Giuliani and Ian Jauslin and Elliott H. Lieb}, journal={Journal of Statistical Physics}, year={2015}, volume={163}, pages={211-238} }

We consider the monomer–dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weights are those on the boundary. We prove a Pfaffian formula for the corresponding partition function. As a consequence of this result, multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics. Our proof is based on the celebrated Kasteleyn theorem, combined with a…

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