2-adic behavior of numbers of domino tilings
The electronic journal of combinatorics, Tome 6 (1999)
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 $n \equiv 0,3 \pmod{4}$.
@article{10_37236_1446,
author = {Henry Cohn},
title = {2-adic behavior of numbers of domino tilings},
journal = {The electronic journal of combinatorics},
year = {1999},
volume = {6},
doi = {10.37236/1446},
zbl = {0913.05036},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1446/}
}
Henry Cohn. 2-adic behavior of numbers of domino tilings. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1446
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