{"id":"https://openalex.org/W2065078485","doi":"https://doi.org/10.1007/bf01844852","title":"Lines, line-point incidences and crossing families in dense sets","display_name":"Lines, line-point incidences and crossing families in dense sets","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2065078485","doi":"https://doi.org/10.1007/bf01844852","mag":"2065078485"},"language":"en","primary_location":{"id":"doi:10.1007/bf01844852","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01844852","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/A5072926305","display_name":"P\u00e1vel Valtr","orcid":"https://orcid.org/0000-0002-3102-4166"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I2800345347","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800345347"]}],"countries":["CZ","DE"],"is_corresponding":true,"raw_author_name":"Pavel Valtr","raw_affiliation_strings":["Department of Applied Mathematics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Praha 1, Czech Republic","Graduiertenkolleg \u201cAlgorithmische Diskrete Mathematik\u201d, Fachbereich Mathematik, Freie Universit\u00e4t Berlin, Takustrasse 9, 14195, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Praha 1, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Graduiertenkolleg \u201cAlgorithmische Diskrete Mathematik\u201d, Fachbereich Mathematik, Freie Universit\u00e4t Berlin, Takustrasse 9, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I2800345347"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072926305"],"corresponding_institution_ids":["https://openalex.org/I21250087","https://openalex.org/I2800345347"],"apc_list":null,"apc_paid":null,"fwci":0.433,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.66292135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"269","last_page":"294"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8507766723632812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7904818058013916},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6525876522064209},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.613309383392334},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.5807768106460571},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46955353021621704},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4684101939201355},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.44402438402175903},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.41284847259521484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26617637276649475},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21276888251304626},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18805590271949768}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8507766723632812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904818058013916},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6525876522064209},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.613309383392334},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.5807768106460571},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46955353021621704},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4684101939201355},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.44402438402175903},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.41284847259521484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26617637276649475},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21276888251304626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18805590271949768},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01844852","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01844852","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1564415453","https://openalex.org/W1642685763","https://openalex.org/W2001242324","https://openalex.org/W2008497801","https://openalex.org/W2060633701","https://openalex.org/W2074709558","https://openalex.org/W2087585583","https://openalex.org/W2097669873","https://openalex.org/W2166961358","https://openalex.org/W4237276646"],"related_works":["https://openalex.org/W4297976568","https://openalex.org/W2962851451","https://openalex.org/W2165434229","https://openalex.org/W2895641489","https://openalex.org/W1557097679","https://openalex.org/W3098813812","https://openalex.org/W1879246310","https://openalex.org/W4245661658","https://openalex.org/W2140901212","https://openalex.org/W2159360218"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
