A lonely weak tile
Combinatorics
2024-12-05 v2
Abstract
The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies \cite{conv}, 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 in \cite{weak} by giving an example of a set which tiles its complement weakly, but is neither spectral, nor a proper tile.
Keywords
Cite
@article{arxiv.2410.04948,
title = {A lonely weak tile},
author = {Gergely Kiss and Itay Londner and Máté Matolcsi and Gábor Somlai},
journal= {arXiv preprint arXiv:2410.04948},
year = {2024}
}