{"id":"https://openalex.org/W2038662421","doi":"https://doi.org/10.1016/s0012-365x(98)00208-8","title":"Union-closed families of sets","display_name":"Union-closed families of sets","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2038662421","doi":"https://doi.org/10.1016/s0012-365x(98)00208-8","mag":"2038662421"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(98)00208-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00208-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete 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/A5032394397","display_name":"Piotr W\u00f3jcik","orcid":null},"institutions":[{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr W\u00f3jcik","raw_affiliation_strings":["Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Pozna\u0144, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032394397"],"corresponding_institution_ids":["https://openalex.org/I59411706"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.1819,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76146132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"199","issue":"1-3","first_page":"173","last_page":"182"},"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":0.9815999865531921,"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":0.9815999865531921,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9146999716758728,"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"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9129999876022339,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/mathematics","display_name":"Mathematics","score":0.9133617877960205},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7378456592559814},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6770291328430176},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5632200837135315},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.5520704388618469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5380752682685852},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.480714350938797},{"id":"https://openalex.org/keywords/maximal-element","display_name":"Maximal element","score":0.4797855019569397},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.4720398187637329},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.2968025505542755},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04835441708564758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04794204235076904}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9133617877960205},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7378456592559814},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6770291328430176},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5632200837135315},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.5520704388618469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5380752682685852},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.480714350938797},{"id":"https://openalex.org/C196773441","wikidata":"https://www.wikidata.org/wiki/Q1475294","display_name":"Maximal element","level":3,"score":0.4797855019569397},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.4720398187637329},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2968025505542755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04835441708564758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04794204235076904},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(98)00208-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(98)00208-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1633614532","https://openalex.org/W1969964326","https://openalex.org/W1993810789","https://openalex.org/W2009296448","https://openalex.org/W2027636325","https://openalex.org/W2092150356","https://openalex.org/W2114722286","https://openalex.org/W2709002772"],"related_works":["https://openalex.org/W4255072571","https://openalex.org/W4312630145","https://openalex.org/W2335628905","https://openalex.org/W2049204673","https://openalex.org/W2072589849","https://openalex.org/W2983070708","https://openalex.org/W4302343495","https://openalex.org/W2284674159","https://openalex.org/W1993810789","https://openalex.org/W2137230158"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}