The number of tiles of $\mathbb{Z}^d$

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Itai Benjamini , Gady Kozma , Elad Tzalik This is my paper · ORCID

classification math.COmath.DSmath.PR

keywords mathbbnumberfracleftprovedrightsubsetstile

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abstract

It is proved that the number of subsets of $[n]^d$ that tile $\mathbb{Z}^d$ is $\left(3^{\frac{1}{3}}\right)^{n^d \pm o(n^d)}$.