{"id":"https://openalex.org/W2106887502","doi":"https://doi.org/10.1007/s00454-008-9113-7","title":"Unavoidable Crossings in a Thinnest Plane Covering with Congruent Convex Disks","display_name":"Unavoidable Crossings in a Thinnest Plane Covering with Congruent Convex Disks","publication_year":2008,"publication_date":"2008-10-03","ids":{"openalex":"https://openalex.org/W2106887502","doi":"https://doi.org/10.1007/s00454-008-9113-7","mag":"2106887502"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-008-9113-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9113-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9113-7.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9113-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078737567","display_name":"Andr\u00e1s Bezdek","orcid":"https://orcid.org/0000-0001-5152-7636"},"institutions":[{"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/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["HU","US"],"is_corresponding":true,"raw_author_name":"Andr\u00e1s Bezdek","raw_affiliation_strings":["MTA R\u00e9nyi Institute, 13-15 R\u00e9altanoda u., Budapest, Hungary","Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA"],"affiliations":[{"raw_affiliation_string":"MTA R\u00e9nyi Institute, 13-15 R\u00e9altanoda u., Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089421531","display_name":"W. Kuperberg","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W\u0142odzimierz Kuperberg","raw_affiliation_strings":["Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078737567"],"corresponding_institution_ids":["https://openalex.org/I127817813","https://openalex.org/I82497590"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09949109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":"2","first_page":"187","last_page":"208"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9993000030517578,"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/combinatorics","display_name":"Combinatorics","score":0.7429360151290894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.740357518196106},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.7024714350700378},{"id":"https://openalex.org/keywords/inscribed-figure","display_name":"Inscribed figure","score":0.568837583065033},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5639314651489258},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5630837678909302},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5558724999427795},{"id":"https://openalex.org/keywords/pentagon","display_name":"Pentagon","score":0.5313580632209778},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4596071243286133},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.43251723051071167},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38759005069732666},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.37102603912353516}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7429360151290894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.740357518196106},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7024714350700378},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.568837583065033},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5639314651489258},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5630837678909302},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5558724999427795},{"id":"https://openalex.org/C2779965921","wikidata":"https://www.wikidata.org/wiki/Q127840","display_name":"Pentagon","level":2,"score":0.5313580632209778},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4596071243286133},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.43251723051071167},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38759005069732666},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.37102603912353516},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-008-9113-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9113-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9113-7.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"}],"best_oa_location":{"id":"doi:10.1007/s00454-008-9113-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-008-9113-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-008-9113-7.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":[{"display_name":"Sustainable cities and communities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2106887502.pdf","grobid_xml":"https://content.openalex.org/works/W2106887502.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W102543617","https://openalex.org/W239990970","https://openalex.org/W324457701","https://openalex.org/W1520007244","https://openalex.org/W1539895965","https://openalex.org/W1581904374","https://openalex.org/W1589055062","https://openalex.org/W1600365026","https://openalex.org/W1996888884","https://openalex.org/W2008614444","https://openalex.org/W2076321155","https://openalex.org/W2313599663","https://openalex.org/W2333442752","https://openalex.org/W2481227236","https://openalex.org/W2912202394"],"related_works":["https://openalex.org/W1970960579","https://openalex.org/W3099884977","https://openalex.org/W2402215390","https://openalex.org/W4297581286","https://openalex.org/W2952368903","https://openalex.org/W4296580083","https://openalex.org/W2949500586","https://openalex.org/W2371177213","https://openalex.org/W1867657303","https://openalex.org/W4386395423"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
