{"id":"https://openalex.org/W2522772211","doi":"https://doi.org/10.1080/10586458.2017.1286273","title":"Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry","display_name":"Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry","publication_year":2017,"publication_date":"2017-03-02","ids":{"openalex":"https://openalex.org/W2522772211","doi":"https://doi.org/10.1080/10586458.2017.1286273","mag":"2522772211"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1286273","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1286273","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.05167","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035030737","display_name":"Fabr\u00edcio Caluza Machado","orcid":"https://orcid.org/0000-0002-9527-3479"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Fabr\u00edcio Caluza Machado","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de Sao Paulo, S\u00e3o Paulo, Brazil","Instituto de Matem\u00e1tica e Estat\u00cdstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de Sao Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00cdstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046618878","display_name":"Fernando M\u00e1rio de Oliveira Filho","orcid":"https://orcid.org/0000-0002-7219-636X"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fernando M\u00e1rio de Oliveira Filho","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de Sao Paulo, S\u00e3o Paulo, Brazil","Instituto de Matem\u00e1tica e Estat\u00cdstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de Sao Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00cdstica, Universidade de S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035030737"],"corresponding_institution_ids":["https://openalex.org/I17974374"],"apc_list":null,"apc_paid":null,"fwci":1.91163731,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82211776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"3","first_page":"362","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9972000122070312,"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":0.9972000122070312,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.9222488403320312},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7238364815711975},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6351033449172974},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.6074901223182678},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5814312100410461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5713511109352112},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5636148452758789},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5562654137611389},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.5452739000320435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3304760456085205},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13482603430747986},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.11168581247329712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08817920088768005},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07337361574172974},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06270641088485718}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.9222488403320312},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7238364815711975},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6351033449172974},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.6074901223182678},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5814312100410461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5713511109352112},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5636148452758789},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5562654137611389},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.5452739000320435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3304760456085205},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13482603430747986},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.11168581247329712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08817920088768005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07337361574172974},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06270641088485718},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2017.1286273","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1286273","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.05167","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.05167","pdf_url":"https://arxiv.org/pdf/1609.05167","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2522772211","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1609.05167v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1609.05167","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.05167","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.05167","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.05167","pdf_url":"https://arxiv.org/pdf/1609.05167","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1487855796","https://openalex.org/W1596185498","https://openalex.org/W1599833186","https://openalex.org/W2013083117","https://openalex.org/W2028783114","https://openalex.org/W2054085030","https://openalex.org/W2055993677","https://openalex.org/W2079565519","https://openalex.org/W2091275975","https://openalex.org/W2101504517","https://openalex.org/W2107996047","https://openalex.org/W2268390549","https://openalex.org/W2584020404","https://openalex.org/W2949537651","https://openalex.org/W2951179629","https://openalex.org/W4251659063","https://openalex.org/W4255317205","https://openalex.org/W4293259454"],"related_works":["https://openalex.org/W2001098796","https://openalex.org/W2031923588","https://openalex.org/W2057575932","https://openalex.org/W1970394054","https://openalex.org/W2951775482","https://openalex.org/W2132400628","https://openalex.org/W2188680895","https://openalex.org/W2020760300","https://openalex.org/W1648726702","https://openalex.org/W2065110770","https://openalex.org/W3100072452","https://openalex.org/W2952690984","https://openalex.org/W2028920274","https://openalex.org/W1541505008","https://openalex.org/W2997850323","https://openalex.org/W2167345674","https://openalex.org/W2130187443","https://openalex.org/W1836227897","https://openalex.org/W2216459995","https://openalex.org/W2964963376"],"abstract_inverted_index":{"The":[0],"kissing":[1,44],"number":[2,8,45],"of":[3,9,31,49],"$\\mathbb{R}^n$":[4],"is":[5],"the":[6,27,37,43,58,62],"maximum":[7],"pairwise-nonoverlapping":[10],"unit":[11,19],"spheres":[12],"that":[13],"can":[14],"simultaneously":[15],"touch":[16],"a":[17],"central":[18],"sphere.":[20],"Mittelmann":[21],"and":[22,33],"Vallentin":[23,34],"(2010),":[24],"based":[25],"on":[26],"semidefinite":[28,63],"programming":[29,64],"bound":[30,65],"Bachoc":[32],"(2008),":[35],"computed":[36],"best":[38],"known":[39],"upper":[40,69],"bounds":[41,70],"for":[42,46,71],"several":[47],"values":[48],"$n":[50,72],"\\leq":[51],"23$.":[52,76],"In":[53],"this":[54],"paper,":[55],"we":[56],"exploit":[57],"symmetry":[59],"present":[60],"in":[61],"to":[66],"provide":[67],"improved":[68],"=":[73],"9,":[74],"\\ldots,":[75]},"counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
