{"id":"https://openalex.org/W2108969732","doi":"https://doi.org/10.1007/s00454-005-1195-x","title":"Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings","display_name":"Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings","publication_year":2005,"publication_date":"2005-10-17","ids":{"openalex":"https://openalex.org/W2108969732","doi":"https://doi.org/10.1007/s00454-005-1195-x","mag":"2108969732"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-005-1195-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1195-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1195-x.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/s00454-005-1195-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005013807","display_name":"Ronald Graham","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ronald L. Graham","raw_affiliation_strings":["Department  of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92110, USA","Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92110, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department  of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92110, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, University of California at San Diego, La Jolla, CA 92110, USA#TAB#","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005612207","display_name":"Jeffrey C. Lagarias","orcid":"https://orcid.org/0000-0002-4157-5527"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey C. Lagarias","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109216874","display_name":"Colin L. Mallows","orcid":null},"institutions":[{"id":"https://openalex.org/I4210137298","display_name":"Avaya (United States)","ror":"https://ror.org/041vyyf82","country_code":"US","type":"company","lineage":["https://openalex.org/I4210137298"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Colin L. Mallows","raw_affiliation_strings":["Avaya Labs, Basking Ridge, NJ 07920, USA","Avaya Labs, Basking Ridge, NJ 07920, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Avaya Labs, Basking Ridge, NJ 07920, USA","institution_ids":["https://openalex.org/I4210137298"]},{"raw_affiliation_string":"Avaya Labs, Basking Ridge, NJ 07920, USA#TAB#","institution_ids":["https://openalex.org/I4210137298"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085031562","display_name":"Allan R. Wilks","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Allan R. Wilks","raw_affiliation_strings":["AT&T Labs, Florham Park, NJ 07932-0971, USA","AT&T Laboratories, Florham Park, NJ 07932-0971, USA"],"affiliations":[{"raw_affiliation_string":"AT&T Labs, Florham Park, NJ 07932-0971, USA","institution_ids":["https://openalex.org/I1283103587"]},{"raw_affiliation_string":"AT&T Laboratories, Florham Park, NJ 07932-0971, USA","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091127513","display_name":"Catherine H. Yan","orcid":"https://orcid.org/0000-0003-0062-5564"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Catherine H. Yan","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005013807"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0266,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.76949778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"35","issue":"1","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circle-packing","display_name":"Circle packing","score":0.8989720344543457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6979431509971619},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6751644015312195},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.6279093027114868},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.48666268587112427},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4544321894645691},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4258015751838684},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13633808493614197}],"concepts":[{"id":"https://openalex.org/C123115066","wikidata":"https://www.wikidata.org/wiki/Q5121501","display_name":"Circle packing","level":2,"score":0.8989720344543457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6979431509971619},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6751644015312195},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6279093027114868},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.48666268587112427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4544321894645691},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4258015751838684},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13633808493614197},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-005-1195-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1195-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1195-x.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"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/41357","is_oa":false,"landing_page_url":"http://hdl.handle.net/2027.42/41357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s00454-005-1195-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1195-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1195-x.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":[],"awards":[{"id":"https://openalex.org/G2739434688","display_name":"Research on Enumerative and Probabilistic Combinatorics","funder_award_id":"0245526","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G299646831","display_name":"Enumerative Combinatorics and Probabilistic Method","funder_award_id":"0070574","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4468279293","display_name":null,"funder_award_id":"DMS-0070574","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6815402834","display_name":"Approximation Algorithms for identification, bin packing and scheduling problems","funder_award_id":"0310991","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7495793209","display_name":null,"funder_award_id":"-0245526","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320323021","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108969732.pdf","grobid_xml":"https://content.openalex.org/works/W2108969732.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W7842899","https://openalex.org/W1502669108","https://openalex.org/W1576071247","https://openalex.org/W1967614538","https://openalex.org/W2055393964","https://openalex.org/W2057101465","https://openalex.org/W2078206416","https://openalex.org/W2114306596","https://openalex.org/W2126357560","https://openalex.org/W2161554729","https://openalex.org/W2167578217","https://openalex.org/W2487407117","https://openalex.org/W2800860906","https://openalex.org/W4285719527","https://openalex.org/W4293217885"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2769125261","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W3190219083","https://openalex.org/W4298053056","https://openalex.org/W2551052552","https://openalex.org/W2949863649","https://openalex.org/W1568242700"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
