The Number of Tiles of $\mathbb{Z}^d$
Abstract
For fixed $d\ge 1$, let $t_{n,d}$ be the number of subsets of$[n]^d$ that tile $\mathbb{Z}^d$ by translations. We prove that\[t_{n,d}=(3^{1/3})^{n^d\pm o(n^d)}.\]
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Bayesian Methods and Mixture Models
Cellular Automata and Applications
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 3
- Publication date
- 7 August 2026
- Language
- EN