On Motzkin’s problem in the circle group

The version of record is available online at: https://doi.org/10.1134/S0081543821040039

Detalles Bibliográficos
Autores: Candela Pokorna, Pablo, Catalá, Carlos, Rué Perna, Juan José|||0000-0002-6420-3179, Serra Albó, Oriol|||0000-0001-8561-4631
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/365095
Acceso en línea:https://hdl.handle.net/2117/365095
https://dx.doi.org/10.1134/S0081543821040039
Access Level:acceso abierto
Palabra clave:Sequences (Mathematics)
Successions (Matemàtica)
Classificació AMS::11 Number theory::11B Sequences and sets
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
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oai_identifier_str oai:upcommons.upc.edu:2117/365095
network_acronym_str ES
network_name_str España
repository_id_str
spelling On Motzkin’s problem in the circle groupCandela Pokorna, PabloCatalá, CarlosRué Perna, Juan José|||0000-0002-6420-3179Serra Albó, Oriol|||0000-0001-8561-4631Sequences (Mathematics)Successions (Matemàtica)Classificació AMS::11 Number theory::11B Sequences and setsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresThe version of record is available online at: https://doi.org/10.1134/S0081543821040039Given a subset D of the interval (0,1), if a Borel set A¿[0,1) contains no pair of elements whose difference modulo 1 is in D, then how large can the Lebesgue measure of A be? This is the analogue in the circle group of a well-known problem of Motzkin, originally posed for sets of integers. We make a first treatment of this circle-group analogue, for finite sets D of missing differences, using techniques from ergodic theory, graph theory and the geometry of numbers. Our results include an exact solution when D has two elements at least one of which is irrational. When every element of D is rational, the problem is equivalent to estimating the independence ratio of a circulant graph. In the case of two rational elements, we give an estimate for this ratio in terms of the odd girth of the graph, which is asymptotically sharp and also recovers the classical solution of Cantor and Gordon to Motzkin’s original problem for two missing differences.Peer Reviewed20212021-09-0120222022-03-31journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/365095https://dx.doi.org/10.1134/S0081543821040039reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3650952026-05-27T15:37:01Z
dc.title.none.fl_str_mv On Motzkin’s problem in the circle group
title On Motzkin’s problem in the circle group
spellingShingle On Motzkin’s problem in the circle group
Candela Pokorna, Pablo
Sequences (Mathematics)
Successions (Matemàtica)
Classificació AMS::11 Number theory::11B Sequences and sets
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
title_short On Motzkin’s problem in the circle group
title_full On Motzkin’s problem in the circle group
title_fullStr On Motzkin’s problem in the circle group
title_full_unstemmed On Motzkin’s problem in the circle group
title_sort On Motzkin’s problem in the circle group
dc.creator.none.fl_str_mv Candela Pokorna, Pablo
Catalá, Carlos
Rué Perna, Juan José|||0000-0002-6420-3179
Serra Albó, Oriol|||0000-0001-8561-4631
author Candela Pokorna, Pablo
author_facet Candela Pokorna, Pablo
Catalá, Carlos
Rué Perna, Juan José|||0000-0002-6420-3179
Serra Albó, Oriol|||0000-0001-8561-4631
author_role author
author2 Catalá, Carlos
Rué Perna, Juan José|||0000-0002-6420-3179
Serra Albó, Oriol|||0000-0001-8561-4631
author2_role author
author
author
dc.subject.none.fl_str_mv Sequences (Mathematics)
Successions (Matemàtica)
Classificació AMS::11 Number theory::11B Sequences and sets
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
topic Sequences (Mathematics)
Successions (Matemàtica)
Classificació AMS::11 Number theory::11B Sequences and sets
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
description The version of record is available online at: https://doi.org/10.1134/S0081543821040039
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-09-01
2022
2022-03-31
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/365095
https://dx.doi.org/10.1134/S0081543821040039
url https://hdl.handle.net/2117/365095
https://dx.doi.org/10.1134/S0081543821040039
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301629

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