Corpus ID: 119615079

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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