{"id":"https://openalex.org/W2149723593","doi":"https://doi.org/10.1016/0097-3165(84)90041-4","title":"The number of different distances determined by n points in the plane","display_name":"The number of different distances determined by n points in the plane","publication_year":1984,"publication_date":"1984-05-01","ids":{"openalex":"https://openalex.org/W2149723593","doi":"https://doi.org/10.1016/0097-3165(84)90041-4","mag":"2149723593"},"language":"en","primary_location":{"id":"doi:10.1016/0097-3165(84)90041-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(84)90041-4","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"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":"Journal of Combinatorial Theory, Series A","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/A5113657664","display_name":"Fan Chung","orcid":"https://orcid.org/0000-0002-6553-7402"},"institutions":[{"id":"https://openalex.org/I4210107053","display_name":"Core Competence","ror":"https://ror.org/012cc0c94","country_code":"US","type":"company","lineage":["https://openalex.org/I4210107053"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F.R.K Chung","raw_affiliation_strings":["Bell Communications Research, Murray Hill, New Jersey 07974 USA"],"affiliations":[{"raw_affiliation_string":"Bell Communications Research, Murray Hill, New Jersey 07974 USA","institution_ids":["https://openalex.org/I4210107053"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113657664"],"corresponding_institution_ids":["https://openalex.org/I4210107053"],"apc_list":{"value":3320,"currency":"USD","value_usd":3320},"apc_paid":null,"fwci":0.7123,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.75280899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"36","issue":"3","first_page":"342","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9948999881744385,"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":0.9948999881744385,"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/T12504","display_name":"Mathematics and Applications","score":0.9851999878883362,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/combinatorics","display_name":"Combinatorics","score":0.7386648654937744},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.7218500375747681},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6805069446563721},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6471138000488281},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5945181250572205},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5134390592575073},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4390064477920532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2546573877334595},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09678977727890015}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7386648654937744},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.7218500375747681},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6805069446563721},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6471138000488281},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5945181250572205},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5134390592575073},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4390064477920532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2546573877334595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09678977727890015},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0097-3165(84)90041-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(84)90041-4","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"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":"Journal of Combinatorial Theory, Series A","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.125.1734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.1734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucsd.edu/~fan/mypaps/fanpap/67distances.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1970934335","https://openalex.org/W2319149236","https://openalex.org/W2327933849","https://openalex.org/W4211205179","https://openalex.org/W4252916111"],"related_works":["https://openalex.org/W4360764540","https://openalex.org/W2378491141","https://openalex.org/W4319874546","https://openalex.org/W4256250254","https://openalex.org/W2549201271","https://openalex.org/W1506630056","https://openalex.org/W4238206434","https://openalex.org/W2897501241","https://openalex.org/W4252675521","https://openalex.org/W187561811"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}