On the structure of multiple translational tilings by polygonal regions
| dc.creator | Kolountzakis, Mihail N. | |
| dc.date | 1999-04-14 | |
| dc.date.accessioned | 2026-07-07T05:28:41Z | |
| dc.date.available | 2026-07-07T05:28:41Z | |
| dc.description | We consider polygons with the following ``pairing property'': for each edge of the polygon there is precisely one other edge parallel to it. We study the problem of when such a polygon $K$ tiles the plane multiply when translated at the locations $Λ$, where $Λ$ is a multiset in the plane. The pairing property of $K$ makes this question particularly amenable to Fourier Analysis. After establishing a necessary and sufficient condition for $K$ to tile with a given lattice $Λ$ (which was first found by Bolle for the case of convex polygons-notice that all convex polygons that tile, necessarily have the pairing property and, therefore, our theorems apply to them) we move on to prove that a large class of such polygons tiles only quasi-periodically, which for us means that $Λ$ must be a finite union of translated 2-dimensional lattices in the plane. For the particular case of convex polygons we show that all convex polygons which are not parallelograms tile necessarily quasi-periodically, if at all. | |
| dc.identifier | https://arxiv.org/abs/math/9904065 | |
| dc.identifier | http://arxiv.org/abs/math/9904065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78353 | |
| dc.subject | Metric Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42 | |
| dc.title | On the structure of multiple translational tilings by polygonal regions | |
| dc.type | text |