# Algebraic Method in Tilings

@article{Hork2016AlgebraicMI, title={Algebraic Method in Tilings}, author={Peter Hor{\'a}k and Dongryul Kim}, journal={arXiv: Combinatorics}, year={2016} }

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$-space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of $n$-space by translates of a cluster $V$ of prime size then there is a lattice tiling by $V$ as well. Finally, we provide supporting evidence for a conjecture that each tiling by translates of a prime size… Expand

#### 3 Citations

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A survey of papers on the Golomb-Welch conjecture is provided and new results on Golomb–WelCh conjecture dealing with perfect Lee codes of large radii are presented. Expand

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