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{\bf Henry Cohn}
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{\bf $2$-adic Behavior of Numbers of Domino Tilings}
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We study the $2$-adic behavior of the number of domino tilings of a
$2n \times 2n$ square as $n$ varies.  It was previously known that
this number was of the form $2^nf(n)^2$, 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 $Z$.  The extension
satisfies the functional equation $f(-1-n) = \pm f(n)$, where the sign
is positive iff $n \equiv 0,3 \pmod{4}$.


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