2-adic behavior of numbers of domino tilings

Details 2-adic behavior of numbers of domino tilings 2-adic behavior of numbers of domino tilings

2000-08-30

arxiv.org/abs/math/0008222v1

Electronic Journal of Combinatorics 6 (1999), #R14

Mathematics

Combinatorics

7 pages

Scientific paper

We study the 2-adic behavior of the number of domino tilings of a 2n-by-2n square as nvaries. It was previously known that this number was of the form 2^n f(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) = +- f(n), where +- sign is + if n is congruent to 0 or 3 modulo 4 and - otherwise.

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