{"id":"https://openalex.org/W7104594712","doi":"https://doi.org/10.1145/3747199.3747575","title":"Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions","display_name":"Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions","publication_year":2025,"publication_date":"2025-07-28","ids":{"openalex":"https://openalex.org/W7104594712","doi":"https://doi.org/10.1145/3747199.3747575"},"language":null,"primary_location":{"id":"doi:10.1145/3747199.3747575","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3747199.3747575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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":null,"display_name":"Diego Armentano","orcid":"https://orcid.org/0000-0003-3752-1670"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":true,"raw_author_name":"Diego Armentano","raw_affiliation_strings":["Facultad de Ciencias Econ\u00f3micas y Administraci\u00f3n, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0000-0003-3752-1670","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Econ\u00f3micas y Administraci\u00f3n, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Leandro Bentancur","orcid":"https://orcid.org/0009-0004-4260-554X"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Leandro Bentancur","raw_affiliation_strings":["Facultad de Ciencias, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0009-0004-4260-554X","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Federico Carrasco","orcid":"https://orcid.org/0009-0006-1018-5741"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Federico Carrasco","raw_affiliation_strings":["Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0009-0006-1018-5741","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Marcelo Fiori","orcid":"https://orcid.org/0000-0002-3732-1778"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Marcelo Fiori","raw_affiliation_strings":["Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0000-0002-3732-1778","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Mat\u00edas Vald\u00e9s","orcid":"https://orcid.org/0009-0000-6497-4574"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Mat\u00edas Vald\u00e9s","raw_affiliation_strings":["Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0009-0000-6497-4574","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mauricio Velasco","orcid":"https://orcid.org/0000-0003-4787-7910"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Mauricio Velasco","raw_affiliation_strings":["Facultad de Ciencias, Universidad de la Rep\u00fablica, Montevideo, Uruguay"],"raw_orcid":"https://orcid.org/0000-0003-4787-7910","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias, Universidad de la Rep\u00fablica, Montevideo, Uruguay","institution_ids":["https://openalex.org/I180910786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180910786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6486173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"309","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2840000092983246,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2840000092983246,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.2409999966621399,"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/T12351","display_name":"Geometry and complex manifolds","score":0.08550000190734863,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.6779000163078308},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6758999824523926},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6158999800682068},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.59579998254776},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5042999982833862},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4885999858379364},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4867999851703644}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7634999752044678},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6779000163078308},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6758999824523926},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6158999800682068},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.59579998254776},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3653999865055084},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3107999861240387},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C97831314","wikidata":"https://www.wikidata.org/wiki/Q6667307","display_name":"Logarithmic growth","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C23719512","wikidata":"https://www.wikidata.org/wiki/Q867345","display_name":"Euclidean domain","level":4,"score":0.2572999894618988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3747199.3747575","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3747199.3747575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W177591266","https://openalex.org/W1585818218","https://openalex.org/W1733405054","https://openalex.org/W2034449459","https://openalex.org/W2044325752","https://openalex.org/W2052885820","https://openalex.org/W2087947797","https://openalex.org/W2128687423","https://openalex.org/W2152345982","https://openalex.org/W2592503220","https://openalex.org/W2963337767","https://openalex.org/W2964018770","https://openalex.org/W2973564755","https://openalex.org/W2988614387","https://openalex.org/W3011859147","https://openalex.org/W3141384256","https://openalex.org/W4366448665"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,16,27,86,89],"logarithmic":[3,43],"Fekete":[4],"problem,":[5],"which":[6],"consists":[7],"of":[8,13,29,32,80,91],"placing":[9],"a":[10,24,93],"fixed":[11],"number":[12],"points":[14,68],"on":[15],"unit":[17],"sphere":[18],"in":[19,22,69,85],"\\(\\mathbb":[20],"{R}^d\\),":[21],"such":[23],"way":[25],"that":[26,41],"product":[28],"all":[30,57],"pairs":[31],"mutual":[33],"Euclidean":[34],"distances":[35],"is":[36,45],"maximized":[37],"or,":[38],"equivalently,":[39],"so":[40],"their":[42],"energy":[44],"minimized.":[46],"Using":[47],"tools":[48],"from":[49],"Computational":[50],"Algebraic":[51],"Geometry,":[52],"we":[53],"find":[54],"and":[55],"classify":[56],"critical":[58],"configurations":[59],"for":[60],"this":[61],"problem":[62],"when":[63],"considering":[64],"at":[65],"most":[66],"six":[67],"every":[70],"dimension":[71],"d.":[72],"In":[73],"particular,":[74],"our":[75],"approach":[76],"gives":[77],"new":[78],"proofs":[79],"several":[81],"key":[82],"results":[83],"appearing":[84],"literature,":[87],"with":[88],"benefit":[90],"using":[92],"unified":[94],"approach.":[95]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-11-10T00:00:00"}