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The density of sets containing large similar copies of finite sets
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dc.contributor.author | Falconer, Kenneth | |
dc.contributor.author | Kovač, Vjekoslav | |
dc.contributor.author | Yavicoli, Alexia | |
dc.date.accessioned | 2021-10-19T14:30:01Z | |
dc.date.available | 2021-10-19T14:30:01Z | |
dc.date.issued | 2022-11-17 | |
dc.identifier.citation | Falconer , K , Kovač , V & Yavicoli , A 2022 , ' The density of sets containing large similar copies of finite sets ' , Journal d'Analyse Mathématique , vol. 148 , no. 1 , pp. 339-359 . https://doi.org/10.1007/s11854-022-0231-6 | en |
dc.identifier.issn | 0021-7670 | |
dc.identifier.other | PURE: 269135153 | |
dc.identifier.other | PURE UUID: cb498bc5-7ca8-42c1-84c0-db7499aedc15 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/2007.03493v1 | |
dc.identifier.other | ORCID: /0000-0001-8823-0406/work/123196745 | |
dc.identifier.other | Scopus: 85142193997 | |
dc.identifier.other | WOS: 000884960700003 | |
dc.identifier.uri | https://hdl.handle.net/10023/24167 | |
dc.description | Funding: VK is supported by the Croatian Science Foundation, project n◦ UIP-2017-05-4129 (MUNHANAP). AY is supported by the Swiss National Science Foundation, grant n◦ P2SKP2 184047. | en |
dc.description.abstract | We prove that if E⊆Rd (d≥2) is a Lebesgue-measurable set with density larger than (n−2) (n−1), then E contains similar copies of every n-point set P at all sufficiently large scales. Moreover, 'sufficiently large' can be taken to be uniform over all P with prescribed size, minimum separation and diameter. On the other hand, we construct an example to show that the density required to guarantee all large similar copies of n-point sets tends to 1 at a rate 1−O(n−1/5log n). | |
dc.format.extent | 21 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal d'Analyse Mathématique | en |
dc.rights | Copyright © 2022, The Hebrew University of Jerusalem. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s11854-022-0231-6. | en |
dc.subject | Pattern | en |
dc.subject | Density | en |
dc.subject | Similarity | en |
dc.subject | Arithmetic progression | en |
dc.subject | Discrepancy | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.title | The density of sets containing large similar copies of finite sets | en |
dc.type | Journal article | en |
dc.description.version | Preprint | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s11854-022-0231-6 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2023-11-17 | |
dc.identifier.url | https://arxiv.org/abs/2007.03493 | en |
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