{"id":"https://openalex.org/W2067172105","doi":"https://doi.org/10.1007/bf01285815","title":"The number of edges of many faces in a line segment arrangement","display_name":"The number of edges of many faces in a line segment arrangement","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2067172105","doi":"https://doi.org/10.1007/bf01285815","mag":"2067172105"},"language":"en","primary_location":{"id":"doi:10.1007/bf01285815","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01285815","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","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/A5042232059","display_name":"Boris Aronov","orcid":"https://orcid.org/0000-0003-3110-4702"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"B. Aronov","raw_affiliation_strings":["DIMACS Center, Rutgers University, 08855, Piscataway, New Jersey, U.S.A","DIMACS Center, Rutgers University, Piscataway, U.S.A"],"affiliations":[{"raw_affiliation_string":"DIMACS Center, Rutgers University, 08855, Piscataway, New Jersey, U.S.A","institution_ids":[]},{"raw_affiliation_string":"DIMACS Center, Rutgers University, Piscataway, U.S.A","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069999967","display_name":"Herbert Edelsbrunner","orcid":"https://orcid.org/0000-0002-9823-6833"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Edelsbrunner","raw_affiliation_strings":["Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, U.S.A","Department of Computer Science, University of Illinois at Urbana Champaign, Urbana, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana Champaign, Urbana, U.S.A","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065368881","display_name":"Leonidas Guibas","orcid":"https://orcid.org/0000-0002-8315-4886"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. J. Guibas","raw_affiliation_strings":["Computer Science Department, Stanford University, and DEC Systems Research Center, 94301, Paolo Alto, California, U.S.A","Computer Science Department, Stanford University, and DEC Systems Research Center, Paolo Alto, U.S.A"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, and DEC Systems Research Center, 94301, Paolo Alto, California, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Computer Science Department, Stanford University, and DEC Systems Research Center, Paolo Alto, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003485384","display_name":"M. Sharir","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"M. Sharir","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, 10012, New York, U.S.A","School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel","Courant Institute of Mathematical Sciences, New York University, New York, U.S.A"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, 10012, New York, U.S.A","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, U.S.A","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042232059"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0026,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.74662881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":"3","first_page":"261","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9979000091552734,"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":0.9976000189781189,"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/mathematics","display_name":"Mathematics","score":0.8160704970359802},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7468305826187134},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5659533739089966},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.495781272649765},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32058778405189514}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8160704970359802},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7468305826187134},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5659533739089966},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.495781272649765},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32058778405189514}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/bf01285815","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01285815","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.1562","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.1562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~michas/aegs.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.299.994","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.994","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~michas/aegs.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.6421","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.6421","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~sharir/aegs.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320327261","display_name":"National Center for Research and Development","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W307932172","https://openalex.org/W1965230032","https://openalex.org/W1977529491","https://openalex.org/W1984529618","https://openalex.org/W1994094252","https://openalex.org/W2009564521","https://openalex.org/W2018858611","https://openalex.org/W2049742898","https://openalex.org/W2058432138","https://openalex.org/W2059759859","https://openalex.org/W2093180282","https://openalex.org/W2120934134","https://openalex.org/W2146306925","https://openalex.org/W4254977685"],"related_works":["https://openalex.org/W4386442742","https://openalex.org/W2353000084","https://openalex.org/W4205730002","https://openalex.org/W2942906518","https://openalex.org/W1623138178","https://openalex.org/W2357946356","https://openalex.org/W180294324","https://openalex.org/W3084509788","https://openalex.org/W2353540264","https://openalex.org/W1992456351"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}