{"id":"https://openalex.org/W2962692047","doi":"https://doi.org/10.1017/s096354831300014x","title":"Freiman Homomorphisms of Random Subsets of","display_name":"Freiman Homomorphisms of Random Subsets of","publication_year":2013,"publication_date":"2013-06-11","ids":{"openalex":"https://openalex.org/W2962692047","doi":"https://doi.org/10.1017/s096354831300014x","mag":"2962692047"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831300014x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831300014x","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/A5020452147","display_name":"Gonzalo Fiz Pontiveros","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"]},{"id":"https://openalex.org/I4210128604","display_name":"Instituto de Pesquisas Jardim Bot\u00e2nico do Rio de Janeiro","ror":"https://ror.org/033xtdz52","country_code":"BR","type":"archive","lineage":["https://openalex.org/I4210128604"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"GONZALO FIZ PONTIVEROS","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil (e-mail:","IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil (e-mail:","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020452147"],"corresponding_institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.2985115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"4","first_page":"592","last_page":"611"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9948999881744385,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9937000274658203,"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/homomorphism","display_name":"Homomorphism","score":0.94013512134552},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7006034255027771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6081275939941406},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4628118574619293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4040520191192627},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08355820178985596}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.94013512134552},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7006034255027771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6081275939941406},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4628118574619293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4040520191192627},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08355820178985596}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096354831300014x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831300014x","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":12,"referenced_works":["https://openalex.org/W1022649828","https://openalex.org/W1533996792","https://openalex.org/W2022933371","https://openalex.org/W2023847659","https://openalex.org/W2037289762","https://openalex.org/W2068871408","https://openalex.org/W2077204415","https://openalex.org/W2102028311","https://openalex.org/W2912209775","https://openalex.org/W2950855856","https://openalex.org/W2977322974","https://openalex.org/W3038100514"],"related_works":["https://openalex.org/W4308159138","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W4327811209","https://openalex.org/W3037616202","https://openalex.org/W2963079901","https://openalex.org/W390508480","https://openalex.org/W2375240985","https://openalex.org/W1979597421","https://openalex.org/W2087709123"],"abstract_inverted_index":{"Given":[0],"a":[1,8,15],"set":[2],"$A\\subset\\mathbb{Z}_{N}$":[3],",":[4,128],"we":[5],"say":[6,56],"that":[7,57,116],"function":[9],"$f\\colon":[10],"A":[11,29,58,79,105,140,157],"\\to":[12],"\\mathbb{Z}_{N}$":[13],"is":[14,59,104,141,158],"Freiman":[16,40,64],"homomorphism":[17],"if":[18,61,117,148],"f(a)":[19],"+":[20,24],"f(b)":[21],"=":[22,32,72,102,150],"f(c)":[23],"f(d)":[25],"whenever":[26],"a,b,c,d":[27],"\u2208":[28],"satisfy":[30],"a+b":[31],"c+d":[33],".":[34,74,89],"This":[35],"notion":[36],"was":[37],"introduced":[38],"by":[39],"in":[41,49],"the":[42,50,62,69,76,94],"1970s,":[43],"and":[44],"plays":[45],"an":[46],"important":[47],"role":[48],"field":[51],"of":[52,68,78,100],"additive":[53],"combinatorics.":[54],"We":[55,90,114],"linear":[60,106,143,159],"only":[63],"homomorphisms":[65],"are":[66,80],"functions":[67],"form":[70],"f(x)":[71],"ax+b":[73],"Suppose":[75],"elements":[77],"chosen":[81],"independently":[82],"at":[83,93],"random,":[84],"each":[85],"with":[86,107,144,160],"probability":[87,109],"p":[88,101,118,149],"shall":[91],"look":[92],"following":[95],"question:":[96],"For":[97],"which":[98],"values":[99],"p(N)":[103],"high":[108,145,161],"as":[110,135],"N":[111,120,123,126,131,136,151],"\u2192":[112,133,137],"\u221e?":[113],"show":[115],"=(2log":[119],"\u2212":[121],"\u03c9(":[122,130],"))":[124],"1/3":[125],"\u22122/3":[127],"where":[129],")":[132],"\u221e":[134],"\u221e,":[138],"then":[139,156],"not":[142],"probability,":[146],"whereas":[147],"\u22121/2+\u03b5":[152],"for":[153],"any":[154],"\u03b5&gt;0":[155],"probability.":[162]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
