A lonely weak tile
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910726193414144 |
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| author | Kiss, Gergely Londner, Itay Matolcsi, Máté Somlai, Gábor |
| author_facet | Kiss, Gergely Londner, Itay Matolcsi, Máté Somlai, Gábor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A lonely weak tile Kiss, Gergely Londner, Itay Matolcsi, Máté Somlai, Gábor Combinatorics 05B45, 42A75, 20K01 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. |
| title | A lonely weak tile |
| topic | Combinatorics 05B45, 42A75, 20K01 |
| url | https://arxiv.org/abs/2410.04948 |