Geodesic
Alternating-sign matrices and domino tilings. II
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 219-234.

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

Summary: We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of $GL( n)$. The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order $n$ but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.
Keywords: tiling, domino, alternating-sign matrix, monotone triangle, representation, square ice 
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     title = {Alternating-sign matrices and domino tilings. {II}},
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Elkies, Noam; Kuperberg, Greg; Larsen, Michael; Propp, James. Alternating-sign matrices and domino tilings. II. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 219-234. http://geodesic.mathdoc.fr/item/JAC_1992__1_3_a4/