{"id":"https://openalex.org/W2039556593","doi":"https://doi.org/10.1016/0012-365x(81)90267-3","title":"On maximal antichains containing no set and its complement","display_name":"On maximal antichains containing no set and its complement","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W2039556593","doi":"https://doi.org/10.1016/0012-365x(81)90267-3","mag":"2039556593"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(81)90267-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(81)90267-3","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/A5007734919","display_name":"G.F. Clements","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G.F. Clements","raw_affiliation_strings":["University of Colorado, Boulder, CO 80309, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado, Boulder, CO 80309, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036105979","display_name":"H. -D. O. F. Gronau","orcid":null},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H.-D.O.F. Gronau","raw_affiliation_strings":["Wilhelm Pieck University, 25 Rostock, German Democratic Republic","Wilhelm Pieck University, 25 Rostock, German Democratic Republic#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wilhelm Pieck University, 25 Rostock, German Democratic Republic","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Wilhelm Pieck University, 25 Rostock, German Democratic Republic#TAB#","institution_ids":["https://openalex.org/I4665924"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":2.0056,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.87552448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"33","issue":"3","first_page":"239","last_page":"247"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9866999983787537,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9836999773979187,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/antichain","display_name":"Antichain","score":0.9355912804603577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8340633511543274},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8121017217636108},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.7266829013824463},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.7057135105133057},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5558105707168579},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4746459126472473},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.2763875424861908}],"concepts":[{"id":"https://openalex.org/C136134351","wikidata":"https://www.wikidata.org/wiki/Q431937","display_name":"Antichain","level":3,"score":0.9355912804603577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8340633511543274},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8121017217636108},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.7266829013824463},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7057135105133057},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5558105707168579},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4746459126472473},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2763875424861908},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(81)90267-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(81)90267-3","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":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1807012990","https://openalex.org/W1972392483","https://openalex.org/W2021557596","https://openalex.org/W2025324955","https://openalex.org/W2043091249","https://openalex.org/W2052840523","https://openalex.org/W2073286344","https://openalex.org/W2079012015","https://openalex.org/W2084913436","https://openalex.org/W2087567316","https://openalex.org/W2097834100","https://openalex.org/W2114513480","https://openalex.org/W2134380705","https://openalex.org/W2224932111","https://openalex.org/W2325408611","https://openalex.org/W2605976634","https://openalex.org/W2891145841","https://openalex.org/W4213147353","https://openalex.org/W6638460549","https://openalex.org/W6663478365"],"related_works":["https://openalex.org/W2062422981","https://openalex.org/W2128746232","https://openalex.org/W2805443446","https://openalex.org/W2048364936","https://openalex.org/W4378765295","https://openalex.org/W2005152920","https://openalex.org/W2952112853","https://openalex.org/W3020196849","https://openalex.org/W3169136406","https://openalex.org/W24519920"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}