Geodesic
Higher dimensional Aztec diamonds and a $(2^d+2)$-vertex model
Journal of Algebraic Combinatorics, Tome 9 (1999) no. 3, pp. 281-293.

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

Summary: Motivated by the close relationship between the number of perfect matchings of the Aztec diamond graph introduced in [5] and the free energy of the square-ice model, we consider a higher dimensional analog of this phenomenon. For d $ge$ 1, we construct d-uniform hypergraphs which generalize the Aztec diamonds and we consider a companion d-dimensional statistical model (called the 2d + 2-vertex model) whose free energy is given by the logarithm of the number of perfect matchings of our hypergraphs. We prove that the limit defining the free energy per site of the 2d + 2-vertex model exists and we obtain bounds for it. As a consequence, we obtain an especially good asymptotical approximation for the number of matchings of our hypergraphs. 
@article{JAC_1999__9_3_a1,
     author = {Ciucu, Mihai},
     title = {Higher dimensional {Aztec} diamonds and a $(2^d+2)$-vertex model},
     journal = {Journal of Algebraic Combinatorics},
     pages = {281--293},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1999__9_3_a1/}
}
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Ciucu, Mihai. Higher dimensional Aztec diamonds and a $(2^d+2)$-vertex model. Journal of Algebraic Combinatorics, Tome 9 (1999) no. 3, pp. 281-293. http://geodesic.mathdoc.fr/item/JAC_1999__9_3_a1/