A lonely weak tile

Kiss, Gergely ORCID: https://orcid.org/0000-0001-5517-5148, Londner, Itay, Matolcsi, Máté ORCID: https://orcid.org/0000-0003-4889-697X and Somlai, Gábor ORCID: https://orcid.org/0000-0001-5761-7579 (2026) A lonely weak tile. Expositiones Mathematicae, 44 (1). DOI 10.1016/j.exmath.2024.125636

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
152kB

Official URL: https://doi.org/10.1016/j.exmath.2024.125636

Abstract

The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies, due to the fact that every spectral set tiles its complement weakly with a suitable Borel measure. In this paper we review the concept of weak tiling, and answer a question raised by Kolountzakis, Lev and Matolcsi, by giving an example of a set T which tiles its complement weakly, but T is neither spectral, nor a proper tile. (c) 2024 Elsevier GmbH. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Item Type:

Article

Uncontrolled Keywords:

Tiling; Spectral set; Weak tiling;

Divisions:

Institute of Data Analytics and Information Systems

Subjects:

Mathematics, Econometrics

Funders:

Hungarian National Foundation for Scientific Research, János Bolyai Research Fellowship

Projects:

K146922, FK 142993, K132097, K146387, 138596, SNN 132625