{"id":"https://openalex.org/W2110938502","doi":"https://doi.org/10.1007/978-3-642-21046-4_11","title":"On the Heilbronn Optimal Configuration of Seven Points in the Square","display_name":"On the Heilbronn Optimal Configuration of Seven Points in the Square","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2110938502","doi":"https://doi.org/10.1007/978-3-642-21046-4_11","mag":"2110938502"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-21046-4_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-21046-4_11","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5058328411","display_name":"Zhenbing Zeng","orcid":"https://orcid.org/0000-0002-9728-1114"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]},{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhenbing Zeng","raw_affiliation_strings":["Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai (China)"],"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai (China)","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100780211","display_name":"Liang-Y\u00fc Chen","orcid":"https://orcid.org/0000-0002-2981-1945"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]},{"id":"https://openalex.org/I4210139618","display_name":"Shanghai Key Laboratory of Trustworthy Computing","ror":"https://ror.org/030qbr085","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139618"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liangyu Chen","raw_affiliation_strings":["Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai (China)"],"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai (China)","institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058328411"],"corresponding_institution_ids":["https://openalex.org/I4210139618","https://openalex.org/I66867065"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.23876872,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"196","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9977999925613403,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/square","display_name":"Square (algebra)","score":0.8389492034912109},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.7212313413619995},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6934599876403809},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6891577243804932},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4535672068595886},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44221845269203186},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3748018741607666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2662574052810669},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15265771746635437}],"concepts":[{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.8389492034912109},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.7212313413619995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6934599876403809},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6891577243804932},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4535672068595886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44221845269203186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3748018741607666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2662574052810669},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15265771746635437},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-21046-4_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-21046-4_11","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W16939786","https://openalex.org/W579842789","https://openalex.org/W1517742237","https://openalex.org/W1562960078","https://openalex.org/W2045790438","https://openalex.org/W2054456839","https://openalex.org/W2102330543","https://openalex.org/W2172186101","https://openalex.org/W2205343714","https://openalex.org/W2429476713","https://openalex.org/W4251403158","https://openalex.org/W4253394114"],"related_works":["https://openalex.org/W3161375928","https://openalex.org/W222989450","https://openalex.org/W2022929595","https://openalex.org/W2798172748","https://openalex.org/W2949900893","https://openalex.org/W2110938502","https://openalex.org/W2886094488","https://openalex.org/W1987762223","https://openalex.org/W2312788834","https://openalex.org/W96152805"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}