{"id":"https://openalex.org/W3158731051","doi":"https://doi.org/10.1017/s0963548321000109","title":"Additive bases via Fourier analysis","display_name":"Additive bases via Fourier analysis","publication_year":2021,"publication_date":"2021-04-29","ids":{"openalex":"https://openalex.org/W3158731051","doi":"https://doi.org/10.1017/s0963548321000109","mag":"3158731051"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548321000109","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000109","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/A5015718961","display_name":"Bodan Arsovski","orcid":"https://orcid.org/0000-0003-3582-9268"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bodan Arsovski","raw_affiliation_strings":["Skopje, North Macedonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Skopje, North Macedonia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015718961"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19595411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"6","first_page":"930","last_page":"941"},"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":0.9972000122070312,"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":0.9972000122070312,"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":0.9865000247955322,"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/T11797","display_name":"graph theory and CDMA systems","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.8506448864936829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.758643388748169},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.7561233639717102},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7135025262832642},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6063452959060669},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5045899152755737},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.48070937395095825},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4673851728439331},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4161282479763031},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.377543568611145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11018067598342896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06997013092041016},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05984678864479065}],"concepts":[{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.8506448864936829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.758643388748169},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.7561233639717102},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7135025262832642},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6063452959060669},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5045899152755737},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.48070937395095825},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4673851728439331},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4161282479763031},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.377543568611145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11018067598342896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06997013092041016},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05984678864479065},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548321000109","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548321000109","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2023859733","https://openalex.org/W2035816523","https://openalex.org/W2081225965","https://openalex.org/W2963182110","https://openalex.org/W2963199462","https://openalex.org/W4298839848","https://openalex.org/W6719455568"],"related_works":["https://openalex.org/W2388953866","https://openalex.org/W2349918401","https://openalex.org/W4230102134","https://openalex.org/W2052916897","https://openalex.org/W2996768723","https://openalex.org/W2808944898","https://openalex.org/W4212895949","https://openalex.org/W4247866870","https://openalex.org/W4249910233","https://openalex.org/W2187658836"],"abstract_inverted_index":{"Abstract":[0],"Extending":[1],"a":[2,18,28,76,79,131],"result":[3],"by":[4],"Alon,":[5],"Linial,":[6],"and":[7,25,98,121,134],"Meshulam":[8],"to":[9,112],"abelian":[10,20],"groups,":[11],"we":[12,107,135],"prove":[13,63],"that":[14,35,64],"if":[15],"G":[16,33,50,59,74,129],"is":[17,27,54,130],"finite":[19],"group":[21],"of":[22,30,32,38,41,58,68,73,78,81,116,139],"exponent":[23],"m":[24,96,119],"S":[26,39,53],"sequence":[29],"elements":[31,48],"such":[34],"any":[36,69],"subsequence":[37],"consisting":[40],"at":[42,83],"least":[43,84],"$$|S|":[44],"-":[45,86],"m\\ln":[46],"|G|$$":[47],"generates":[49],",":[51],"then":[52],"an":[55],"additive":[56,66],"basis":[57],".":[60],"We":[61],"also":[62],"the":[65,109,126],"span":[67],"l":[70],"generating":[71],"sets":[72],"contains":[75],"coset":[77],"subgroup":[80],"size":[82],"$$|G{|^{1":[85],"c{":[87],"\\in":[88,100,102,123],"^l}}}$$":[89],"for":[90],"certain":[91],"c":[92,94,117],"=":[93,101],"(":[95,118],")":[97,120],"$$":[99,122],"(m)":[103],"&lt;":[104],"1$$":[105],";":[106],"use":[108],"probabilistic":[110],"method":[111],"give":[113,136],"sharper":[114],"values":[115],"(m)$$":[124],"in":[125],"case":[127],"when":[128],"vector":[132],"space;":[133],"new":[137],"proofs":[138],"related":[140],"known":[141],"results.":[142]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
