{"id":"https://openalex.org/W4403306372","doi":"https://doi.org/10.1080/10586458.2024.2410964","title":"Local Configurations in Union-Closed Families","display_name":"Local Configurations in Union-Closed Families","publication_year":2024,"publication_date":"2024-10-10","ids":{"openalex":"https://openalex.org/W4403306372","doi":"https://doi.org/10.1080/10586458.2024.2410964"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2024.2410964","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2024.2410964","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5070329454","display_name":"Jonad Pulaj","orcid":"https://orcid.org/0000-0002-5741-7187"},"institutions":[{"id":"https://openalex.org/I141720752","display_name":"Davidson College","ror":"https://ror.org/02f7k4z58","country_code":"US","type":"education","lineage":["https://openalex.org/I141720752"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonad Pulaj","raw_affiliation_strings":["Department of Mathematics and Computer Science, Davidson College","Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Davidson College","institution_ids":["https://openalex.org/I141720752"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA","institution_ids":["https://openalex.org/I141720752"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082400896","display_name":"Kenan Wood","orcid":null},"institutions":[{"id":"https://openalex.org/I141720752","display_name":"Davidson College","ror":"https://ror.org/02f7k4z58","country_code":"US","type":"education","lineage":["https://openalex.org/I141720752"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kenan Wood","raw_affiliation_strings":["Department of Mathematics and Computer Science, Davidson College","Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Davidson College","institution_ids":["https://openalex.org/I141720752"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA","institution_ids":["https://openalex.org/I141720752"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082400896"],"corresponding_institution_ids":["https://openalex.org/I141720752"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14960324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"4","first_page":"719","last_page":"727"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8468799591064453},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3548746705055237},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3531695604324341}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468799591064453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3548746705055237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3531695604324341}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.2024.2410964","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2024.2410964","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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":11,"referenced_works":["https://openalex.org/W1480909796","https://openalex.org/W1993810789","https://openalex.org/W2022700105","https://openalex.org/W2114722286","https://openalex.org/W2138776194","https://openalex.org/W2785044350","https://openalex.org/W3175444848","https://openalex.org/W3211222374","https://openalex.org/W4316038036","https://openalex.org/W6741128425","https://openalex.org/W6810882043"],"related_works":["https://openalex.org/W4391375266","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"],"abstract_inverted_index":{"The":[0],"Frankl":[1],"or":[2],"Union-Closed":[3],"Sets":[4],"conjecture":[5,104,126],"states":[6],"that":[7,33,89],"for":[8,82,127],"any":[9,90],"finite":[10],"union-closed":[11,58,91],"family":[12,92],"of":[13,30,40,53,65,98,108,120,132],"sets":[14,42],"F":[15,31],"containing":[16,93],"some":[17,22],"nonempty":[18],"set,":[19],"there":[20],"is":[21,35],"element":[23,107],"i":[24,34],"in":[25,36,43,57],"the":[26,41,83,125],"ground":[27],"set":[28],"U(F):=\u222aS\u2208FS":[29],"such":[32,88],"at":[37],"least":[38,84],"half":[39],"F.":[44],"In":[45],"this":[46],"work,":[47],"we":[48,61,76,111],"answer":[49],"an":[50,99,106],"older":[51],"question":[52,68],"Vaughan":[54],"regarding":[55],"symmetry":[56],"families":[59],"and":[60,73,80],"give":[62],"a":[63,66,118],"proof":[64],"recent":[67],"posed":[69],"by":[70],"Ellis,":[71],"Ivan":[72],"Leader.":[74],"Additionally,":[75],"find":[77],"new":[78],"values":[79],"bounds":[81],"integer":[85],"FC(k,":[86,94],"n)":[87,95],"distinct":[96],"k-sets":[97],"n-set":[100],"X":[101],"satisfies":[102],"Frankl\u2019s":[103],"with":[105],"X.":[109],"Finally,":[110],"introduce":[112],"novel":[113],"local":[114],"configuration":[115],"criteria":[116],"through":[117],"generalization":[119],"Poonen\u2019s":[121],"theorem":[122],"to":[123],"prove":[124],"many,":[128],"previously":[129],"unknown":[130],"classes":[131],"families.":[133]},"counts_by_year":[],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
