English

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

Combinatorics 2023-03-15 v1 Dynamical Systems Probability

Abstract

It is proved that the number of subsets of [n]d[n]^d that tile Zd\mathbb{Z}^d is (313)nd±o(nd)\left(3^{\frac{1}{3}}\right)^{n^d \pm o(n^d)}.

Keywords

Cite

@article{arxiv.2303.07956,
  title  = {The number of tiles of $\mathbb{Z}^d$},
  author = {Itai Benjamini and Gady Kozma and Elad Tzalik},
  journal= {arXiv preprint arXiv:2303.07956},
  year   = {2023}
}