An approximate structure theorem for small sumsets

Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA and PB with the same common difference and cardinalities approximately Ks/2. The...

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Detalhes bibliográficos
Autores: Campos, Marcelo, Coulson, Matthew John, Serra Albó, Oriol|||0000-0001-8561-4631, Wötzel, Maximilian|||0000-0001-7591-0998
Formato: capítulo de livro
Fecha de publicación:2021
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/369273
Acesso em linha:https://hdl.handle.net/2117/369273
https://dx.doi.org/10.1007/978-3-030-83823-2_88
Access Level:acceso abierto
Palavra-chave:Sequences (Mathematics)
Additive combinatorics
Sumsets
Hypergraph containers
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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spelling An approximate structure theorem for small sumsetsCampos, MarceloCoulson, Matthew JohnSerra Albó, Oriol|||0000-0001-8561-4631Wötzel, Maximilian|||0000-0001-7591-0998Sequences (Mathematics)Additive combinatoricsSumsetsHypergraph containersSuccessions (Matemàtica)Classificació AMS::11 Number theory::11B Sequences and setsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresLet A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA and PB with the same common difference and cardinalities approximately Ks/2. The result holds for s=¿(log3n) and 2=K=o(s/log3n). Our main tool is an asymmetric version of the method of hypergraph containers which was recently used by Campos to prove the result in the special case A=B.Peer ReviewedBirkhäuser20212021-08-2420222022-06-29book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/2117/369273https://dx.doi.org/10.1007/978-3-030-83823-2_88reponame: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:2117/3692732026-05-27T15:37:01Z
dc.title.none.fl_str_mv An approximate structure theorem for small sumsets
title An approximate structure theorem for small sumsets
spellingShingle An approximate structure theorem for small sumsets
Campos, Marcelo
Sequences (Mathematics)
Additive combinatorics
Sumsets
Hypergraph containers
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 An approximate structure theorem for small sumsets
title_full An approximate structure theorem for small sumsets
title_fullStr An approximate structure theorem for small sumsets
title_full_unstemmed An approximate structure theorem for small sumsets
title_sort An approximate structure theorem for small sumsets
dc.creator.none.fl_str_mv Campos, Marcelo
Coulson, Matthew John
Serra Albó, Oriol|||0000-0001-8561-4631
Wötzel, Maximilian|||0000-0001-7591-0998
author Campos, Marcelo
author_facet Campos, Marcelo
Coulson, Matthew John
Serra Albó, Oriol|||0000-0001-8561-4631
Wötzel, Maximilian|||0000-0001-7591-0998
author_role author
author2 Coulson, Matthew John
Serra Albó, Oriol|||0000-0001-8561-4631
Wötzel, Maximilian|||0000-0001-7591-0998
author2_role author
author
author
dc.subject.none.fl_str_mv Sequences (Mathematics)
Additive combinatorics
Sumsets
Hypergraph containers
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)
Additive combinatorics
Sumsets
Hypergraph containers
Successions (Matemàtica)
Classificació AMS::11 Number theory::11B Sequences and sets
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
description Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA and PB with the same common difference and cardinalities approximately Ks/2. The result holds for s=¿(log3n) and 2=K=o(s/log3n). Our main tool is an asymmetric version of the method of hypergraph containers which was recently used by Campos to prove the result in the special case A=B.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-08-24
2022
2022-06-29
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/369273
https://dx.doi.org/10.1007/978-3-030-83823-2_88
url https://hdl.handle.net/2117/369273
https://dx.doi.org/10.1007/978-3-030-83823-2_88
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.publisher.none.fl_str_mv Birkhäuser
publisher.none.fl_str_mv Birkhäuser
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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