Geodesic
Graphical condensation, overlapping Pfaffians and superpositions of matchings
The electronic journal of combinatorics, Tome 17 (2010)

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The purpose of this paper is to exhibit clearly how the "graphical condensation" identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn–Percus method for the enumeration of matchings. Knuth termed the relevant identities "overlapping Pfaffian" identities and the key concept of proof "superpositions of matchings". In our uniform presentation of the material, we also give an apparently unpublished general "overlapping Pfaffian" identity of Krattenthaler.
DOI : 10.37236/355
Classification : 05C70, 05A19, 05E99 
Markus Fulmek. Graphical condensation, overlapping Pfaffians and superpositions of matchings. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/355
@article{10_37236_355,
     author = {Markus Fulmek},
     title = {Graphical condensation, overlapping {Pfaffians} and superpositions of matchings},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/355},
     zbl = {1215.05131},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/355/}
}
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