Squares and their centers

Autores
Keleti, Tamas; Nagy, Daniel; Shmerkin, Pablo Sebastian
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the relationship between the size of two sets B, S ⊂ R2, when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, Hausdorff dimension, packing dimension, or upper or lower box dimension. Perhaps surprisingly, the results vary depending on the notion of size under consideration. For example, we construct a compact set B of Hausdorff dimension 1 which contains the boundary of an axes-parallel square with center in every point in [0, 1]2, prove that such a B must have packing and lower box dimension at least 7/4, and show by example that this is sharp. For more general sets of centers, the answers for packing and box counting dimensions also differ. These problems are inspired by the analogous problems for circles that were investigated by Bourgain, Marstrand and Wolff, among others.
Fil: Keleti, Tamas. Eötvös Loránd University; Hungría
Fil: Nagy, Daniel. Eötvös University; Argentina
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Materia
Squares
Square Vertices
Hausdorff dimension
box dimension
packing dimension
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/99274
Acceder
id CONICETDig_a401bcf7335d7d2a3337ab3e8081321d
oai_identifier_str oai:ri.conicet.gov.ar:11336/99274
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Squares and their centersKeleti, TamasNagy, DanielShmerkin, Pablo SebastianSquaresSquare VerticesHausdorff dimensionbox dimensionpacking dimensionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the relationship between the size of two sets B, S ⊂ R2, when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, Hausdorff dimension, packing dimension, or upper or lower box dimension. Perhaps surprisingly, the results vary depending on the notion of size under consideration. For example, we construct a compact set B of Hausdorff dimension 1 which contains the boundary of an axes-parallel square with center in every point in [0, 1]2, prove that such a B must have packing and lower box dimension at least 7/4, and show by example that this is sharp. For more general sets of centers, the answers for packing and box counting dimensions also differ. These problems are inspired by the analogous problems for circles that were investigated by Bourgain, Marstrand and Wolff, among others.Fil: Keleti, Tamas. Eötvös Loránd University; HungríaFil: Nagy, Daniel. Eötvös University; ArgentinaFil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaSpringer2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/99274Keleti, Tamas; Nagy, Daniel; Shmerkin, Pablo Sebastian; Squares and their centers; Springer; Journal d'Analyse Mathématique; 134; 2; 2-2018; 643-6690021-7670CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11854-018-0021-3info:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-018-0021-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:33Zoai:ri.conicet.gov.ar:11336/99274instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:38:33.709CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Squares and their centers
title Squares and their centers
spellingShingle Squares and their centers
Keleti, Tamas
Squares
Square Vertices
Hausdorff dimension
box dimension
packing dimension
title_short Squares and their centers
title_full Squares and their centers
title_fullStr Squares and their centers
title_full_unstemmed Squares and their centers
title_sort Squares and their centers
dc.creator.none.fl_str_mv Keleti, Tamas
Nagy, Daniel
Shmerkin, Pablo Sebastian
author Keleti, Tamas
author_facet Keleti, Tamas
Nagy, Daniel
Shmerkin, Pablo Sebastian
author_role author
author2 Nagy, Daniel
Shmerkin, Pablo Sebastian
author2_role author
author
dc.subject.none.fl_str_mv Squares
Square Vertices
Hausdorff dimension
box dimension
packing dimension
topic Squares
Square Vertices
Hausdorff dimension
box dimension
packing dimension
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the relationship between the size of two sets B, S ⊂ R2, when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, Hausdorff dimension, packing dimension, or upper or lower box dimension. Perhaps surprisingly, the results vary depending on the notion of size under consideration. For example, we construct a compact set B of Hausdorff dimension 1 which contains the boundary of an axes-parallel square with center in every point in [0, 1]2, prove that such a B must have packing and lower box dimension at least 7/4, and show by example that this is sharp. For more general sets of centers, the answers for packing and box counting dimensions also differ. These problems are inspired by the analogous problems for circles that were investigated by Bourgain, Marstrand and Wolff, among others.
Fil: Keleti, Tamas. Eötvös Loránd University; Hungría
Fil: Nagy, Daniel. Eötvös University; Argentina
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
description We study the relationship between the size of two sets B, S ⊂ R2, when B contains either the whole boundary or the four vertices of a square with axes-parallel sides and center in every point of S. Size refers to cardinality, Hausdorff dimension, packing dimension, or upper or lower box dimension. Perhaps surprisingly, the results vary depending on the notion of size under consideration. For example, we construct a compact set B of Hausdorff dimension 1 which contains the boundary of an axes-parallel square with center in every point in [0, 1]2, prove that such a B must have packing and lower box dimension at least 7/4, and show by example that this is sharp. For more general sets of centers, the answers for packing and box counting dimensions also differ. These problems are inspired by the analogous problems for circles that were investigated by Bourgain, Marstrand and Wolff, among others.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/99274
Keleti, Tamas; Nagy, Daniel; Shmerkin, Pablo Sebastian; Squares and their centers; Springer; Journal d'Analyse Mathématique; 134; 2; 2-2018; 643-669
0021-7670
CONICET Digital
CONICET
url http://hdl.handle.net/11336/99274
identifier_str_mv Keleti, Tamas; Nagy, Daniel; Shmerkin, Pablo Sebastian; Squares and their centers; Springer; Journal d'Analyse Mathématique; 134; 2; 2-2018; 643-669
0021-7670
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11854-018-0021-3
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-018-0021-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613219112452096
score 13.070432

Publicaciones similares