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

Anna Galluccio, Martin Loebl
1998 Electronic Journal of Combinatorics  
Kasteleyn stated that the generating function of the perfect matchings of a graph of genus $g$ may be written as a linear combination of $4^g$ Pfaffians. Here we prove this statement. As a consequence we present a combinatorial way to compute the permanent of a square matrix.
doi:10.37236/1438 fatcat:kmpcl3dipzdcjg4qydlalshjey