We study the 2-adic behavior of the number of domino tilings of a 2n× 2n square as n varies. It was previously known that this number was of the form 2nf(n)2, where f(n) is an odd, positive integer. We show that the function f is uniformly continuous under the 2-adic metric, and thus extends to a function on all of . The extension satisfies the functional equation f(−1 − n) = ±f(n), where the sign is positive iff n ≡ 0, 3 (mod 4). Kasteleyn [K], and Temperley and Fisher [TF], proved that the… CONTINUE READING