{"id":"https://openalex.org/W2485937216","doi":"https://doi.org/10.1016/0012-365x(82)90199-6","title":"A decomposition theorem for \u03c71-convex sets","display_name":"A decomposition theorem for \u03c71-convex sets","publication_year":1982,"publication_date":"1982-01-01","ids":{"openalex":"https://openalex.org/W2485937216","doi":"https://doi.org/10.1016/0012-365x(82)90199-6","mag":"2485937216"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(82)90199-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(82)90199-6","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/A5055251002","display_name":"Marilyn Breen","orcid":"https://orcid.org/0000-0002-0990-6816"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marilyn Breen","raw_affiliation_strings":["University of Oklahoma, Department of Mathematics, 601 Elm Avenue, Norman, OK 73019, USA"],"affiliations":[{"raw_affiliation_string":"University of Oklahoma, Department of Mathematics, 601 Elm Avenue, Norman, OK 73019, USA","institution_ids":["https://openalex.org/I8692664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055251002"],"corresponding_institution_ids":["https://openalex.org/I8692664"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30585383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"2","first_page":"131","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9973999857902527,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9104999899864197,"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/T12137","display_name":"Economic theories and models","score":0.9017999768257141,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8960402011871338},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6255162954330444},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.612296998500824},{"id":"https://openalex.org/keywords/decomposition-theorem","display_name":"Decomposition theorem","score":0.6056113839149475},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5656101703643799},{"id":"https://openalex.org/keywords/danskins-theorem","display_name":"Danskin's theorem","score":0.5464370250701904},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5200338363647461},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.463716983795166},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.46271321177482605},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.2698705792427063},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.2335433065891266},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.21803149580955505}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8960402011871338},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6255162954330444},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.612296998500824},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.6056113839149475},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5656101703643799},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.5464370250701904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5200338363647461},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.463716983795166},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.46271321177482605},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.2698705792427063},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.2335433065891266},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.21803149580955505},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(82)90199-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(82)90199-6","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":6,"referenced_works":["https://openalex.org/W1966163705","https://openalex.org/W2021313445","https://openalex.org/W2027671115","https://openalex.org/W2043441716","https://openalex.org/W2319564106","https://openalex.org/W6660963041"],"related_works":["https://openalex.org/W2376997122","https://openalex.org/W2026600343","https://openalex.org/W4288324104","https://openalex.org/W2351069524","https://openalex.org/W2039410269","https://openalex.org/W212391553","https://openalex.org/W4233172824","https://openalex.org/W4234856521","https://openalex.org/W2049688189","https://openalex.org/W3021881116"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
