English

2-adic behavior of numbers of domino tilings

Combinatorics 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0008222,
  title  = {2-adic behavior of numbers of domino tilings},
  author = {Henry Cohn},
  journal= {arXiv preprint arXiv:math/0008222},
  year   = {2007}
}

Comments

7 pages