Algebraic Method in Tilings
Combinatorics
2016-03-02 v1
Abstract
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 -space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of -space by translates of a cluster of prime size then there is a lattice tiling by as well. Finally, we provide supporting evidence for a conjecture that each tiling by translates of a prime size cluster is lattice if generates -space.
Keywords
Cite
@article{arxiv.1603.00051,
title = {Algebraic Method in Tilings},
author = {Peter Horak and Dongryul Kim},
journal= {arXiv preprint arXiv:1603.00051},
year = {2016}
}