Geodesic
Perfect matchings of cellular graphs
Journal of Algebraic Combinatorics, Tome 5 (1996) no. 2, pp. 87-103.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce a family of graphs, called cellular, and consider the problem of enumerating their perfect matchings. We prove that the number of perfect matchings of a cellular graph equals a power of 2 times the number of perfect matchings of a certain subgraph, called the core of the graph. This yields, as a special case, a new proof of the fact that the Aztec diamond graph of order $n$ introduced by Elkies, Kuperberg, Larsen and Propp has exactly $2 ^{ n( n+1)/2}$ perfect matchings. As further applications, we prove a recurrence for the number of perfect matchings of certain cellular graphs indexed by partitions, and we enumerate the perfect matchings of two other families of graphs called Aztec rectangles and Aztec triangles.
Keywords: perfect matching, alternating sign pattern, ferrers diagram 
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     title = {Perfect matchings of cellular graphs},
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Ciucu, Mihai. Perfect matchings of cellular graphs. Journal of Algebraic Combinatorics, Tome 5 (1996) no. 2, pp. 87-103. http://geodesic.mathdoc.fr/item/JAC_1996__5_2_a6/