{"id":"https://openalex.org/W2156569826","doi":"https://doi.org/10.1017/s0963548300000870","title":"Constructing Small Sets that are Uniform in Arithmetic Progressions","display_name":"Constructing Small Sets that are Uniform in Arithmetic Progressions","publication_year":1993,"publication_date":"1993-12-01","ids":{"openalex":"https://openalex.org/W2156569826","doi":"https://doi.org/10.1017/s0963548300000870","mag":"2156569826"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300000870","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300000870","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5008113826","display_name":"Alexander Razborov","orcid":null},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. Razborov","raw_affiliation_strings":["Steklov Mathematical Institute, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Steklov Mathematical Institute, Moscow, Russia","institution_ids":["https://openalex.org/I2801160905"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110644008","display_name":"Endre Szemer\u00e9di","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Szemer\u00e9di","raw_affiliation_strings":["Rutgers University, New Brunswick N. J., USA"],"affiliations":[{"raw_affiliation_string":"Rutgers University, New Brunswick N. J., USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"A. Wigderson","raw_affiliation_strings":["Hebrew University, Jerusalem, Israel"],"affiliations":[{"raw_affiliation_string":"Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008113826"],"corresponding_institution_ids":["https://openalex.org/I2801160905"],"apc_list":null,"apc_paid":null,"fwci":0.7736,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.70706006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"4","first_page":"513","last_page":"518"},"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":0.9987000226974487,"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":0.9987000226974487,"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":0.9710000157356262,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9537000060081482,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.8574039936065674},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6963464617729187},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6848406791687012},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.6574273705482483},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6161638498306274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5742993950843811},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39982834458351135},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37520334124565125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29186251759529114}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8574039936065674},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6963464617729187},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6848406791687012},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.6574273705482483},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6161638498306274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5742993950843811},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39982834458351135},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37520334124565125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29186251759529114},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548300000870","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300000870","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.3091","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.3091","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mi.ras.ru/~razborov/interval.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.297.4079","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.4079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.uchicago.edu/~razborov/files/interval.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.645","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.645","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/RAZBOROV/SHIFTS/JOURNAL/final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1595828591","https://openalex.org/W1971019328","https://openalex.org/W2011095973","https://openalex.org/W2011320860","https://openalex.org/W2051758697","https://openalex.org/W2057648657","https://openalex.org/W2070913436","https://openalex.org/W2086156863","https://openalex.org/W2151089248","https://openalex.org/W2151436648","https://openalex.org/W4212904170","https://openalex.org/W4242529138","https://openalex.org/W4253594684","https://openalex.org/W6652937116","https://openalex.org/W6664990114","https://openalex.org/W6667985490","https://openalex.org/W6682411615","https://openalex.org/W6682822356","https://openalex.org/W6835576149"],"related_works":["https://openalex.org/W2196131019","https://openalex.org/W2112041331","https://openalex.org/W2070522125","https://openalex.org/W2924691597","https://openalex.org/W1507520630","https://openalex.org/W2963283366","https://openalex.org/W2171984564","https://openalex.org/W2046580399","https://openalex.org/W2032687362","https://openalex.org/W3169095672"],"abstract_inverted_index":{"For":[0],"every":[1,26],"integer":[2],"N":[3,13,16,30],",":[4],"we":[5],"explicitly":[6],"construct":[7],"a":[8],"subset":[9],"of":[10,14],"residues":[11],"mod":[12],"size(log":[15],")":[17],"o":[18],"(1)":[19],"which":[20],"is":[21],"nearly":[22],"uniformly":[23],"distributed":[24],"in":[25],"arithmetic":[27],"progression":[28],"modulo":[29],".":[31]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
