{"id":"https://openalex.org/W2036209050","doi":"https://doi.org/10.1007/s00454-012-9439-z","title":"Notes About the Carath\u00e9odory Number","display_name":"Notes About the Carath\u00e9odory Number","publication_year":2012,"publication_date":"2012-07-19","ids":{"openalex":"https://openalex.org/W2036209050","doi":"https://doi.org/10.1007/s00454-012-9439-z","mag":"2036209050"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-012-9439-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9439-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9439-z.pdf","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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9439-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Imre B\u00e1r\u00e1ny","orcid":null},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","HU"],"is_corresponding":true,"raw_author_name":"Imre B\u00e1r\u00e1ny","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England","R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England","institution_ids":["https://openalex.org/I45129253"]},{"raw_affiliation_string":"R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":null,"display_name":"Roman Karasev","orcid":null},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]},{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Roman Karasev","raw_affiliation_strings":["Dept. of Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, 141700, Russia","Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya st. 14, Yaroslavl, 150000, Russia"],"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, 141700, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya st. 14, Yaroslavl, 150000, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I127817813","https://openalex.org/I45129253","https://openalex.org/I7597260"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.4208,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87878788,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"3","first_page":"783","last_page":"792"},"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":0.15539999306201935,"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":0.15539999306201935,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.14020000398159027,"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"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.12039999663829803,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/regular-polygon","display_name":"Regular polygon","score":0.4115000069141388},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.2870999872684479},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2606000006198883},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.2451000064611435},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.23659999668598175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5879999995231628},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4309999942779541},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4115000069141388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3474000096321106},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2451000064611435},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.23659999668598175},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.2363000065088272},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.23589999973773956}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-012-9439-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9439-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9439-z.pdf","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:1112.5942","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1112.5942","pdf_url":"https://arxiv.org/pdf/1112.5942","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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.757.9978","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.757.9978","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1112.5942.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-012-9439-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9439-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9439-z.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1372924494","display_name":null,"funder_award_id":"267195","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G2299215204","display_name":null,"funder_award_id":"10-01-00096","funder_id":"https://openalex.org/F4320321648","funder_display_name":"Dynasty Foundation"},{"id":"https://openalex.org/G3515221061","display_name":null,"funder_award_id":"G34.31.0053","funder_id":"https://openalex.org/F4320321648","funder_display_name":"Dynasty Foundation"},{"id":"https://openalex.org/G6471918000","display_name":null,"funder_award_id":"G34.31.0053","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G7594043005","display_name":null,"funder_award_id":"00139","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G8280676509","display_name":null,"funder_award_id":"10-01-00096","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320321648","display_name":"Dynasty Foundation","ror":"https://ror.org/044hrt695"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036209050.pdf","grobid_xml":"https://content.openalex.org/works/W2036209050.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W41805086","https://openalex.org/W136694183","https://openalex.org/W1969197833","https://openalex.org/W1977098616","https://openalex.org/W1978858779","https://openalex.org/W1983127118","https://openalex.org/W1984879308","https://openalex.org/W1994709142","https://openalex.org/W1997817602","https://openalex.org/W2001223605","https://openalex.org/W2004331157","https://openalex.org/W2049678150","https://openalex.org/W2049710017","https://openalex.org/W2061269184","https://openalex.org/W2103307323","https://openalex.org/W2132220587","https://openalex.org/W4235381922","https://openalex.org/W6602595485"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
