We introduce a family of planar regions, called Aztec diamonds, and study the
ways in which these regions can be tiled by dominoes. Our main result is a
generating function that not only gives the number of domino tilings of the
Aztec diamond of order n but also provides information about the orientation
of the dominoes (vertical versus horizontal) and the accessibility of one
tiling from another by means of local modifications. Several proofs of the
formula are given. The problem turns out to have connections with the
alternating sign matrices of Mills, Robbins, and Rumsey, as well as the square
ice model studied by Lieb
