{"id":"https://openalex.org/W3193900015","doi":"https://doi.org/10.1137/22m1511801","title":"The Typical Approximate Structure of Sets with Bounded Sumset","display_name":"The Typical Approximate Structure of Sets with Bounded Sumset","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W3193900015","doi":"https://doi.org/10.1137/22m1511801","mag":"3193900015"},"language":"en","primary_location":{"id":"doi:10.1137/22m1511801","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1511801","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030221569","display_name":"Marcelo Campos","orcid":null},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Marcelo Campos","raw_affiliation_strings":["Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, RJ, 22460-320, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, RJ, 22460-320, Brazil","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079186550","display_name":"Matthew Coulson","orcid":"https://orcid.org/0000-0002-2877-2913"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Matthew Coulson","raw_affiliation_strings":["Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063949199","display_name":"Oriol Serra","orcid":"https://orcid.org/0000-0001-8561-4631"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Oriol Serra","raw_affiliation_strings":["Department of Mathematics, Universitat Polit\u00e8cnica de Catalunya, 08034 Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitat Polit\u00e8cnica de Catalunya, 08034 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048407815","display_name":"Maximilian W\u00f6tzel","orcid":"https://orcid.org/0000-0001-7591-0998"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Maximilian W\u00f6tzel","raw_affiliation_strings":["Korteweg-de Vries Institute for Mathematics, Universiteit van Amsterdam, 1098 XG Amsterdam, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-7591-0998","affiliations":[{"raw_affiliation_string":"Korteweg-de Vries Institute for Mathematics, Universiteit van Amsterdam, 1098 XG Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315","https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030221569"],"corresponding_institution_ids":["https://openalex.org/I141883831"],"apc_list":null,"apc_paid":null,"fwci":0.6696,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5173449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"37","issue":"3","first_page":"1386","last_page":"1418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8944754004478455},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7331799268722534},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.6969881057739258},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6315128207206726},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5773317813873291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5483822822570801},{"id":"https://openalex.org/keywords/structured-program-theorem","display_name":"Structured program theorem","score":0.4476989209651947}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8944754004478455},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7331799268722534},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6969881057739258},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6315128207206726},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5773317813873291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5483822822570801},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.4476989209651947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1511801","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1511801","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2547691996","display_name":null,"funder_award_id":"MTM2017-82166-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G3412787705","display_name":null,"funder_award_id":"OCENW.M20.009","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6366911711","display_name":null,"funder_award_id":"MDM-2014-0445-16-2","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6374332334","display_name":null,"funder_award_id":"MDM-2014-0445","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G7282214104","display_name":null,"funder_award_id":"PRE2018-083621","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G8250324087","display_name":null,"funder_award_id":"PID2020-113082GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1481615827","https://openalex.org/W1552645429","https://openalex.org/W1555768633","https://openalex.org/W1818472233","https://openalex.org/W1964044820","https://openalex.org/W1967030660","https://openalex.org/W1983665367","https://openalex.org/W2025194749","https://openalex.org/W2026568457","https://openalex.org/W2028369791","https://openalex.org/W2031357976","https://openalex.org/W2034548735","https://openalex.org/W2034838716","https://openalex.org/W2076061548","https://openalex.org/W2091329824","https://openalex.org/W2095600968","https://openalex.org/W2171162943","https://openalex.org/W2171213162","https://openalex.org/W2342433841","https://openalex.org/W2773806639","https://openalex.org/W2806327269","https://openalex.org/W2974183384","https://openalex.org/W2981411081","https://openalex.org/W3012130915","https://openalex.org/W3038100514","https://openalex.org/W3102216609","https://openalex.org/W3103069393","https://openalex.org/W3154744885","https://openalex.org/W3195051109","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W1498930646","https://openalex.org/W4311629248","https://openalex.org/W2949631035","https://openalex.org/W2069842544","https://openalex.org/W2085276333","https://openalex.org/W4250921304","https://openalex.org/W4252753165","https://openalex.org/W2624065397","https://openalex.org/W2525865568"],"abstract_inverted_index":{"Let":[0],"and":[1,27,35,41,64],"be":[2],"randomly":[3],"chosen":[4],"subsets":[5],"of":[6,11,54,73,76],"the":[7,37,74,90],"first":[8],"positive":[9],"integers":[10],"cardinalities":[12,42],",":[13],"such":[14,52],"that":[15,23],"their":[16],"sumset":[17],"has":[18],"size":[19],".":[20,44,65,93],"We":[21,45],"show":[22],"asymptotically":[24],"almost":[25,29],"surely":[26],"are":[28],"fully":[30],"contained":[31],"in":[32,56,89],"arithmetic":[33],"progressions":[34],"with":[36],"same":[38],"common":[39],"difference":[40],"approximately":[43],"also":[46],"prove":[47,86],"a":[48],"counting":[49],"theorem":[50],"for":[51,63],"pairs":[53],"sets":[55],"arbitrary":[57],"abelian":[58],"groups.":[59],"The":[60],"results":[61,88],"hold":[62],"Our":[66],"main":[67],"tool":[68],"is":[69],"an":[70],"asymmetric":[71],"version":[72],"method":[75],"hypergraph":[77],"containers":[78],"which":[79],"was":[80],"recently":[81],"used":[82],"by":[83],"Campos":[84],"to":[85],"similar":[87],"special":[91],"case":[92]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}