On 2-adic behavior of the number of domino tilings on torus
DOI:
https://doi.org/10.11575/cdm.v14i1.62673Abstract
We study the 2-adic behavior of the number of domino tilings of a $2(2n+1)\times 2(2n+1)$ torus. We show that this number is of the form $2^{4n+3}g(n)^2+2^{8n+2}(2n+1)^{4n}h(n)$, where $g(n)$ and $h(n)$ are odd positive integers. Moreover, we prove that $g(n)$ and $h(n)$ are uniformly continuous under the 2-adic metric and invariant under interchanging $n$ and $-1-n$. This paper is an analogy of Henry Cohn's results for $2n\times 2n$ squares (Electron. J. Combin. 6 (1999)).
References
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