A New Simple Proof of the Aztec Diamond Theorem

摘要

The Aztec diamond of order n is the union of lattice squares in the plane intersecting the square . The Aztec diamond theorem states that the number of domino tilings of this shape is . It was first proved by Elkies et al. (J. Algebraic Comb. 1(2):111-132, 1992). We give a new simple proof of this theorem.