{"id":"https://openalex.org/W2412178246","doi":"https://doi.org/10.1007/s00454-017-9935-2","title":"On Sets Defining Few Ordinary Planes","display_name":"On Sets Defining Few Ordinary Planes","publication_year":2017,"publication_date":"2017-09-19","ids":{"openalex":"https://openalex.org/W2412178246","doi":"https://doi.org/10.1007/s00454-017-9935-2","mag":"2412178246"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-017-9935-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-017-9935-2","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1606.02138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040387138","display_name":"Simeon Ball","orcid":"https://orcid.org/0000-0003-4845-2084"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Simeon Ball","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Jordi Girona 1-3 M\u00f2dul C3, Campus Nord, 08034, Barcelona, Spain","Departament de Matem\u00e0tiques Universitat Polit\u00e8cnica de Catalunya  Barcelona Spain"],"raw_orcid":"https://orcid.org/0000-0003-4845-2084","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Jordi Girona 1-3 M\u00f2dul C3, Campus Nord, 08034, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques Universitat Polit\u00e8cnica de Catalunya  Barcelona Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040387138"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.4497,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82472753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"60","issue":"1","first_page":"220","last_page":"253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9962000250816345,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/prism","display_name":"Prism","score":0.8379131555557251},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7077460289001465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6435115337371826},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6032785177230835},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5989885926246643},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5832532048225403},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.48419883847236633},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4714157283306122},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4448878765106201},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44374990463256836},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37513333559036255},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.317655086517334},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.19511377811431885}],"concepts":[{"id":"https://openalex.org/C67666897","wikidata":"https://www.wikidata.org/wiki/Q165896","display_name":"Prism","level":2,"score":0.8379131555557251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7077460289001465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6435115337371826},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6032785177230835},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5989885926246643},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5832532048225403},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.48419883847236633},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4714157283306122},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4448878765106201},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44374990463256836},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37513333559036255},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.317655086517334},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.19511377811431885},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s00454-017-9935-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-017-9935-2","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.02138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.02138","pdf_url":"https://arxiv.org/pdf/1606.02138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},{"id":"pmh:oai:dnet:upcommonspor::8b123fcab602da7d880f99a2f85103b3","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/111528","pdf_url":"http://hdl.handle.net/2117/111528","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/updatedVersion"},{"id":"mag:2412178246","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1606.02138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:upcommons.upc.edu:2117/111528","is_oa":false,"landing_page_url":"https://hdl.handle.net/2117/111528","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1606.02138","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.02138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1606.02138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.02138","pdf_url":"https://arxiv.org/pdf/1606.02138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2745536041","display_name":null,"funder_award_id":"MTM2014-54745-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1597380673","https://openalex.org/W1989891936","https://openalex.org/W2005650866","https://openalex.org/W2028771266","https://openalex.org/W2046939500","https://openalex.org/W2053849387","https://openalex.org/W2061788258","https://openalex.org/W2319518804","https://openalex.org/W2489723062","https://openalex.org/W2506035431","https://openalex.org/W3172100879","https://openalex.org/W4235244481"],"related_works":["https://openalex.org/W2963195447","https://openalex.org/W2887750833","https://openalex.org/W2506035431","https://openalex.org/W1938593961","https://openalex.org/W2086165124","https://openalex.org/W2142660837","https://openalex.org/W2745207010","https://openalex.org/W2072869041","https://openalex.org/W2097950202","https://openalex.org/W2062399637","https://openalex.org/W1669572421","https://openalex.org/W1597717682","https://openalex.org/W1584992860","https://openalex.org/W1554571931","https://openalex.org/W2087146362","https://openalex.org/W2002988261","https://openalex.org/W2394762589","https://openalex.org/W1976841046","https://openalex.org/W3124527033","https://openalex.org/W2119373505"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
