{"id":"https://openalex.org/W4248232393","doi":"https://doi.org/10.2178/jsl/1203350785","title":"Flag algebras","display_name":"Flag algebras","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W4248232393","doi":"https://doi.org/10.2178/jsl/1203350785"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1203350785","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1203350785","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","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/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Alexander A. Razborov","raw_affiliation_strings":["School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. E-mail:","Steklov Mathematical Institute, Moscow, Russia. E-mail:"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA. E-mail:","institution_ids":["https://openalex.org/I40036882"]},{"raw_affiliation_string":"Steklov Mathematical Institute, Moscow, Russia. E-mail:","institution_ids":["https://openalex.org/I2801160905"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008113826"],"corresponding_institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I40036882"],"apc_list":null,"apc_paid":null,"fwci":4.7898,"has_fulltext":false,"cited_by_count":181,"citation_normalized_percentile":{"value":0.95461095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"72","issue":"4","first_page":"1239","last_page":"1282"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.9988999962806702,"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":0.9973000288009644,"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/mathematics","display_name":"Mathematics","score":0.7112569808959961},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6582804322242737},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5752918720245361},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5419929027557373},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41698628664016724}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7112569808959961},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6582804322242737},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5752918720245361},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5419929027557373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41698628664016724},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1203350785","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1203350785","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1203350785","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1203350785","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"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/W1552744309","https://openalex.org/W1684722273","https://openalex.org/W1999613943","https://openalex.org/W2049005199","https://openalex.org/W2076011470","https://openalex.org/W2078321205","https://openalex.org/W2115730400","https://openalex.org/W2323590783","https://openalex.org/W2770196964","https://openalex.org/W2901284226","https://openalex.org/W2911938838","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W2963966623"],"abstract_inverted_index":{"Abstract":[0],"Asymptotic":[1],"extremal":[2],"combinatorics":[3],"deals":[4],"with":[5,54,150],"questions":[6],"that":[7,47,107],"in":[8,112,147],"the":[9,45,67,113,123,141],"language":[10],"of":[11,24,52,126,135,145],"model":[12],"theory":[13,27],"can":[14],"be":[15,44],"re-stated":[16],"as":[17],"follows.":[18],"For":[19],"finite":[20],"models":[21,93],"M,":[22,41],"N":[23,42,53,74,81],"an":[25],"universal":[26],"without":[28],"constants":[29],"and":[30,94,118],"function":[31],"symbols":[32],"(like":[33],"graphs,":[34],"digraphs":[35],"or":[36],"hypergraphs),":[37],"let":[38],"p":[39,69,76],"(":[40,70,77],")":[43],"probability":[46],"a":[48,104,131,136,148],"randomly":[49],"chosen":[50],"sub-model":[51],"\u2223M\u2223":[55],"elements":[56],"is":[57],"isomorphic":[58],"to":[59,97],"M":[60,71,78,84,87],".":[61],"Which":[62],"asymptotic":[63],"relations":[64],"exist":[65],"between":[66],"quantities":[68],"1":[72,85,88],",":[73,80,89],"),\u2026,":[75],"h":[79],"),":[82],"where":[83],",\u2026,":[86],"are":[90],"fixed":[91],"\u201ctemplate\u201d":[92],"\u2223N\u2223":[95],"grows":[96],"infinity?":[98],"In":[99],"this":[100,127],"paper":[101],"we":[102],"develop":[103],"formal":[105],"calculus":[106],"captures":[108],"many":[109],"standard":[110],"arguments":[111],"area,":[114],"both":[115],"previously":[116],"known":[117],"apparently":[119],"new.":[120],"We":[121],"give":[122],"first":[124],"application":[125],"formalism":[128],"by":[129,138],"presenting":[130],"new":[132],"simple":[133],"proof":[134],"result":[137],"Fisher":[139],"about":[140],"minimal":[142],"possible":[143],"density":[144],"triangles":[146],"graph":[149],"given":[151],"edge":[152],"density.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2022-05-12T00:00:00"}