On the Theory of Pfaffian Orientations. I. Perfect Matchings and Permanents

@article{Galluccio1999OnTT,
  title={On the Theory of Pfaffian Orientations. I. Perfect Matchings and Permanents},
  author={Anna Galluccio and Martin Loebl},
  journal={Electr. J. Comb.},
  year={1999},
  volume={6}
}
Kasteleyn stated that the generating function of the perfect matchings of a graph of genus g may be written as a linear combination of 4 Pfaffians. Here we prove this statement. As a consequence we present a combinatorial way to compute the permanent of a square matrix. Mathematical Reviews Subject Numbers 05B35, 05C15, 05A15 ∗Supported by NATO-CNR Fellowship †Supported by DONET, GACR 0194 and GAUK 194 

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