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arXiv · 2410.04948

A lonely weak tile

Gergely Kiss·Itay Londner·Máté Matolcsi·Gábor Somlai
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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 $T$ which tiles its complement weakly, but $T$ is neither spectral, nor a proper tile.

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Gergely Kiss, Itay Londner, Máté Matolcsi, Gábor Somlai. 2024-12-03. A lonely weak tile. https://arxiv.org/abs/2410.04948

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