{"id":"https://openalex.org/W2014727454","doi":"https://doi.org/10.1090/s0025-5718-96-00765-x","title":"On sequences without geometric progressions","display_name":"On sequences without geometric progressions","publication_year":1996,"publication_date":"1996-10-01","ids":{"openalex":"https://openalex.org/W2014727454","doi":"https://doi.org/10.1090/s0025-5718-96-00765-x","mag":"2014727454"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00765-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00765-x","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012885184","display_name":"Brienne Elisabeth Brown","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brienne Brown","raw_affiliation_strings":["9211 Mintwood Street, Silver Spring, Maryland 20901"],"affiliations":[{"raw_affiliation_string":"9211 Mintwood Street, Silver Spring, Maryland 20901","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085783796","display_name":"Daniel M. Gordon","orcid":"https://orcid.org/0000-0003-4373-3637"},"institutions":[{"id":"https://openalex.org/I4210157118","display_name":"CCI Reprographics (United States)","ror":"https://ror.org/04d7j1v83","country_code":"US","type":"company","lineage":["https://openalex.org/I4210157118"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Gordon","raw_affiliation_strings":["Center for Communications Research, 4320 Westerra Court San Diego, California 92121"],"affiliations":[{"raw_affiliation_string":"Center for Communications Research, 4320 Westerra Court San Diego, California 92121","institution_ids":["https://openalex.org/I4210157118"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012885184"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.14429791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"65","issue":"216","first_page":"1749","last_page":"1754"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9987000226974487,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9984999895095825,"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/mathematics","display_name":"Mathematics","score":0.8664339780807495},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6290106773376465},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6195014119148254},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.5187132954597473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35861319303512573},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2819070816040039}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8664339780807495},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6290106773376465},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6195014119148254},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.5187132954597473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35861319303512573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2819070816040039},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-96-00765-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00765-x","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.104.3107","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.3107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ccrwest.org/gordon/math_comp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.105.652","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.2811","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.2811","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.4152","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.4152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ccrwest.org/gordon/math_comp.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00765-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00765-x","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00765-X/S0025-5718-96-00765-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2014727454.pdf","grobid_xml":"https://content.openalex.org/works/W2014727454.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1022649828","https://openalex.org/W1555475515","https://openalex.org/W1992497946","https://openalex.org/W2009196521","https://openalex.org/W2047878384","https://openalex.org/W2108900323","https://openalex.org/W4246167497"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2935909890","https://openalex.org/W2778153218","https://openalex.org/W2758277628","https://openalex.org/W1531601525","https://openalex.org/W1979597421"],"abstract_inverted_index":{"Several":[0],"papers":[1],"have":[2,6],"investigated":[3],"sequences":[4,31,42,62,94],"which":[5],"no":[7],"<inline-formula":[8,44,65],"content-type=\"math/mathml\">":[9,45,66],"<mml:math":[10,46,67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,47,68],"alttext=\"k\">":[12,48,69],"<mml:semantics>":[13,49,70],"<mml:mi>k</mml:mi>":[14,50,71],"<mml:annotation":[15,51,72],"encoding=\"application/x-tex\">k</mml:annotation>":[16,52,73],"</mml:semantics>":[17,53,74],"</mml:math>":[18,54,75],"</inline-formula>":[19,55,76],"-term":[20,56],"arithmetic":[21],"progressions,":[22,58],"finding":[23],"bounds":[24],"on":[25,85],"their":[26],"density":[27],"and":[28,59,91],"looking":[29,40],"at":[30,41,93],"generated":[32,95],"by":[33,96],"greedy":[34,98],"algorithms.":[35],"Rankin":[36],"in":[37],"1960":[38],"suggested":[39],"without":[43],"geometric":[57],"constructed":[60],"such":[61],"for":[63],"each":[64],"with":[77],"positive":[78],"density.":[79],"In":[80],"this":[81],"paper":[82],"we":[83],"improve":[84],"Rankin\u2019s":[86],"results,":[87],"derive":[88],"upper":[89],"bounds,":[90],"look":[92],"a":[97],"algorithm.":[99]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}