{"id":"https://openalex.org/W1548285263","doi":"https://doi.org/10.37236/4656","title":"An improved lower bound related to the Furstenberg-S\u00e1rk\u00f6zy theorem","display_name":"An improved lower bound related to the Furstenberg-S\u00e1rk\u00f6zy theorem","publication_year":2015,"publication_date":"2015-02-16","ids":{"openalex":"https://openalex.org/W1548285263","doi":"https://doi.org/10.37236/4656","mag":"1548285263"},"language":"en","primary_location":{"id":"doi:10.37236/4656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p32/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026968428","display_name":"Mark Lewko","orcid":null},"institutions":[{"id":"https://openalex.org/I2799798094","display_name":"UCLA Health","ror":"https://ror.org/01d88se56","country_code":"US","type":"funder","lineage":["https://openalex.org/I2799798094"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mark Lewko","raw_affiliation_strings":["UCLA","UCLA ,"],"affiliations":[{"raw_affiliation_string":"UCLA","institution_ids":["https://openalex.org/I2799798094"]},{"raw_affiliation_string":"UCLA ,","institution_ids":["https://openalex.org/I2799798094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026968428"],"corresponding_institution_ids":["https://openalex.org/I2799798094"],"apc_list":null,"apc_paid":null,"fwci":0.6771,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62569409,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11476","display_name":"Graph theory and applications","score":0.9815000295639038,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8425997495651245},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8299547433853149},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.72502601146698},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.7234678268432617},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5834627151489258},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.50113844871521},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34822899103164673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1498810052871704},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14787152409553528}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8425997495651245},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8299547433853149},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.72502601146698},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.7234678268432617},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5834627151489258},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.50113844871521},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34822899103164673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1498810052871704},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14787152409553528},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.675.8425","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.675.8425","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v22i1p32/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/4656","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4656","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1548285263.pdf","grobid_xml":"https://content.openalex.org/works/W1548285263.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1596624097","https://openalex.org/W1970366772","https://openalex.org/W1976236259","https://openalex.org/W2023600080","https://openalex.org/W2055155904","https://openalex.org/W2062279398","https://openalex.org/W2093806925","https://openalex.org/W2114487569","https://openalex.org/W2183091601","https://openalex.org/W2318342593","https://openalex.org/W2949871485","https://openalex.org/W2964304010","https://openalex.org/W3100139723","https://openalex.org/W3105325455","https://openalex.org/W3138287827","https://openalex.org/W4233633270","https://openalex.org/W4241397309","https://openalex.org/W6633621516","https://openalex.org/W6718866609","https://openalex.org/W6826470420","https://openalex.org/W6828676903","https://openalex.org/W6832476291"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W4287273005","https://openalex.org/W3135784370","https://openalex.org/W2776473626","https://openalex.org/W1966028935","https://openalex.org/W2151482654","https://openalex.org/W24519920","https://openalex.org/W4253000595","https://openalex.org/W2087778462"],"abstract_inverted_index":{"Let":[0],"$D(n)$":[1],"denote":[2],"the":[3,6,10,15,37],"cardinality":[4],"of":[5,9,17,20,29],"largest":[7],"subset":[8],"set":[11],"$\\{1,2,\\ldots,n\\}$":[12],"such":[13],"that":[14,34,43],"difference":[16],"no":[18],"pair":[19],"distinct":[21],"elements":[22],"is":[23],"a":[24],"square.":[25],"A":[26],"well-known":[27],"theorem":[28],"Furstenberg":[30],"and":[31],"S\u00e1rk\u00f6zy":[32],"states":[33],"$D(n)=o(n)$.":[35],"In":[36],"other":[38],"direction,":[39],"Ruzsa":[40],"has":[41],"proven":[42],"$D(n)":[44],"\\gtrsim":[45],"n^{\\gamma}$":[46],"for":[47],"$\\gamma":[48,63],"=":[49,64],"\\frac{1}{2}\\left(":[50,65],"1":[51,66],"+":[52,67],"\\frac{\\log":[53,68],"7}{\\log":[54],"65}":[55],"\\right)":[56,71],"\\approx":[57,72],"0.733077$.":[58],"We":[59],"improve":[60],"this":[61],"to":[62],"12}{\\log":[69],"205}":[70],"0.733412$.":[73]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}