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For questions about mathematical tiling.

42 votes
2 answers
2k views

Does any set of dominoes tile some common figure?

Some related polyomino tiling problems are known to be NP-complete, and some are even undecidable. So, this question could also appear to be not so 'elementary' as it might look. …
Arsenii Sagdeev's user avatar
12 votes
0 answers
166 views

Can the optimal packing density in $\mathbb{Z}^d$ be irrational?

For a finite $S \subset \mathbb{Z}^d$, let $d_p(S)$ be its optimal packing density. That is, the maximal lower asymptotic density of $A+S$, where $A \subset \mathbb{Z}^d$ is such that $(a_1+S)\cap (a_ …
Arsenii Sagdeev's user avatar