{"id":"https://openalex.org/W2083328260","doi":"https://doi.org/10.1007/s00454-013-9542-9","title":"The Set of Packing and Covering Densities of Convex Disks","display_name":"The Set of Packing and Covering Densities of Convex Disks","publication_year":2013,"publication_date":"2013-09-27","ids":{"openalex":"https://openalex.org/W2083328260","doi":"https://doi.org/10.1007/s00454-013-9542-9","mag":"2083328260"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-013-9542-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-013-9542-9","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"W\u0142odzimierz Kuperberg","raw_affiliation_strings":["Department of Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA","Department of Mathematics and Statistics, Auburn University, Auburn, USA 36849-5310#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, Auburn University, Auburn, AL, 36849-5310, USA","institution_ids":["https://openalex.org/I82497590"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Auburn University, Auburn, USA 36849-5310#TAB#","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089421531"],"corresponding_institution_ids":["https://openalex.org/I82497590"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4716,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65802794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"4","first_page":"1072","last_page":"1084"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9987000226974487,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9965000152587891,"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":0.7537021636962891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6845709085464478},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.62574702501297},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5144832134246826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28242868185043335},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20850813388824463}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7537021636962891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6845709085464478},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.62574702501297},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5144832134246826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28242868185043335},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20850813388824463},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-013-9542-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-013-9542-9","pdf_url":null,"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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W102543617","https://openalex.org/W239990970","https://openalex.org/W1589055062","https://openalex.org/W1970219143","https://openalex.org/W1976664838","https://openalex.org/W1980583519","https://openalex.org/W2003213208","https://openalex.org/W2033074315","https://openalex.org/W2049017086","https://openalex.org/W2159130720","https://openalex.org/W2159376961","https://openalex.org/W2313242147","https://openalex.org/W2314598295","https://openalex.org/W2333442752","https://openalex.org/W2613907538","https://openalex.org/W4240853087","https://openalex.org/W4244655342","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"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"}