Geodesic
On the theory of Pfaffian orientations. I: Perfect matchings and permanents
The electronic journal of combinatorics, Tome 6 (1999)
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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
Classification : 05A15, 05C30
Mots-clés : generating function, perfect matching, Pfaffian, genus 
@article{10_37236_1438,
     author = {Anna Galluccio and Martin Loebl},
     title = {On the theory of {Pfaffian} orientations. {I:} {Perfect} matchings and permanents},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1438},
     zbl = {0909.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1438/}
}
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Anna Galluccio; Martin Loebl. On the theory of Pfaffian orientations. I: Perfect matchings and permanents. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1438

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