{"id":"https://openalex.org/W2040913719","doi":"https://doi.org/10.1007/s00454-008-9122-6","title":"Recurrence Relationships for the Mean Number of\u00a0Faces and Vertices for Random Convex Hulls","display_name":"Recurrence Relationships for the Mean Number of\u00a0Faces and Vertices for Random Convex Hulls","publication_year":2008,"publication_date":"2008-11-18","ids":{"openalex":"https://openalex.org/W2040913719","doi":"https://doi.org/10.1007/s00454-008-9122-6","mag":"2040913719"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-008-9122-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9122-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9122-6.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 & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9122-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005349239","display_name":"Richard Cowan","orcid":"https://orcid.org/0000-0001-9816-7316"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Richard Cowan","raw_affiliation_strings":["School of Mathematics and Statistics, University of Sydney, NSW 2006, Sydney, Australia","University of Sydney, School of Mathematics and Statistics, NSW 2006, Sydney, Australia#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Sydney, NSW 2006, Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"University of Sydney, School of Mathematics and Statistics, NSW 2006, Sydney, Australia#TAB#","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005349239"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4357,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61061626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"43","issue":"2","first_page":"209","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9997000098228455,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9901999831199646,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9628999829292297,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8713711500167847},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.8458251953125},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8250932693481445},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.6297069787979126},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.6256543397903442},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5787597298622131},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.43649420142173767},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.4206116795539856},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.3182283341884613},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12986508011817932},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.09382864832878113}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8713711500167847},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8458251953125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8250932693481445},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.6297069787979126},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6256543397903442},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5787597298622131},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.43649420142173767},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.4206116795539856},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3182283341884613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12986508011817932},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.09382864832878113},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-008-9122-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9122-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9122-6.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 & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-008-9122-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9122-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9122-6.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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2040913719.pdf","grobid_xml":"https://content.openalex.org/works/W2040913719.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W565214016","https://openalex.org/W1607203414","https://openalex.org/W1979832469","https://openalex.org/W1985426635","https://openalex.org/W1985633322","https://openalex.org/W2008872259","https://openalex.org/W2043395048","https://openalex.org/W2044097246","https://openalex.org/W2059272894","https://openalex.org/W2069472046","https://openalex.org/W2117218580","https://openalex.org/W2319567436","https://openalex.org/W2334311386","https://openalex.org/W4210631977","https://openalex.org/W4235610653","https://openalex.org/W4237697075","https://openalex.org/W4242060431","https://openalex.org/W4253948983"],"related_works":["https://openalex.org/W2300145982","https://openalex.org/W2365830408","https://openalex.org/W2580512045","https://openalex.org/W981962503","https://openalex.org/W4214795209","https://openalex.org/W868123585","https://openalex.org/W2017227406","https://openalex.org/W2371177213","https://openalex.org/W2374624997","https://openalex.org/W2093765879"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}