Tilings of $\mathbb{Z}$ with multisets of distances

Andrey Kupavskii, Elizaveta Popova

In this paper, we study tilings of $\mathbb{Z}$, that is, coverings of $\mathbb{Z}$ by disjoint sets (tiles). Let $T=\{d_1,\dots ,d_s\}$ be a given multiset of distances. Is it alwa…