{"id":"https://openalex.org/W1900535273","doi":"https://doi.org/10.37236/3784","title":"On Limits of Dense Packing of Equal Spheres in a Cube","display_name":"On Limits of Dense Packing of Equal Spheres in a Cube","publication_year":2015,"publication_date":"2015-02-16","ids":{"openalex":"https://openalex.org/W1900535273","doi":"https://doi.org/10.37236/3784","mag":"1900535273"},"language":"en","primary_location":{"id":"doi:10.37236/3784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p35/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p35/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019077826","display_name":"Milos Tatarevic","orcid":null},"institutions":[{"id":"https://openalex.org/I2802536887","display_name":"College of Alameda","ror":"https://ror.org/00vaf6k96","country_code":"US","type":"education","lineage":["https://openalex.org/I2802536887","https://openalex.org/I4210142450"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Milos Tatarevic","raw_affiliation_strings":["Alameda, CA 94501, U.S.A"],"affiliations":[{"raw_affiliation_string":"Alameda, CA 94501, U.S.A","institution_ids":["https://openalex.org/I2802536887"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019077826"],"corresponding_institution_ids":["https://openalex.org/I2802536887"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05905376,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9692999720573425,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9692999720573425,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9631999731063843,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9592000246047974,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.902003288269043},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.8839384317398071},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6811458468437195},{"id":"https://openalex.org/keywords/packing-problems","display_name":"Packing problems","score":0.4829922914505005},{"id":"https://openalex.org/keywords/close-packing-of-equal-spheres","display_name":"Close-packing of equal spheres","score":0.4371795058250427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42168158292770386},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3430723547935486},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20102569460868835}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.902003288269043},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.8839384317398071},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6811458468437195},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.4829922914505005},{"id":"https://openalex.org/C177825532","wikidata":"https://www.wikidata.org/wiki/Q1037840","display_name":"Close-packing of equal spheres","level":2,"score":0.4371795058250427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42168158292770386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3430723547935486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20102569460868835},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/3784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p35/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.07933","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.07933","pdf_url":"https://arxiv.org/pdf/1503.07933","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":"","raw_type":"text"},{"id":"mag:1900535273","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1503.07933","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":"pmh:oai:CiteSeerX.psu:10.1.1.675.7524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.675.7524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v22i1p35/pdf/","raw_type":"text"},{"id":"doi:10.48550/arxiv.1503.07933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.07933","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-journal"}],"best_oa_location":{"id":"doi:10.37236/3784","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3784","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p35/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1900535273.pdf","grobid_xml":"https://content.openalex.org/works/W1900535273.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1586932739","https://openalex.org/W1669649303","https://openalex.org/W1965660671","https://openalex.org/W2040634226","https://openalex.org/W2045958904","https://openalex.org/W2073931801","https://openalex.org/W2086548836","https://openalex.org/W2115874935","https://openalex.org/W2119492068","https://openalex.org/W6677941113","https://openalex.org/W6816829675"],"related_works":["https://openalex.org/W2934370908","https://openalex.org/W2305766087","https://openalex.org/W2992657610","https://openalex.org/W2979643164","https://openalex.org/W2081780875","https://openalex.org/W1970082954","https://openalex.org/W2058544037","https://openalex.org/W1983799802","https://openalex.org/W2028167818","https://openalex.org/W1975627189","https://openalex.org/W2069907252","https://openalex.org/W2123550204","https://openalex.org/W2073489177","https://openalex.org/W2321781616","https://openalex.org/W2089717132","https://openalex.org/W2085711360","https://openalex.org/W2949392325","https://openalex.org/W2036995457","https://openalex.org/W3106464822","https://openalex.org/W2016114328"],"abstract_inverted_index":{"We":[0,73],"examine":[1],"packing":[2],"of":[3,19,28,35,49,53,81],"$n$":[4,11],"congruent":[5],"spheres":[6,20,54],"in":[7,21],"a":[8,22,45,50],"cube":[9],"when":[10],"is":[12],"close":[13],"but":[14],"less":[15],"than":[16],"the":[17,37,57],"number":[18,52],"regular":[23],"cubic":[24],"close-packed":[25],"(ccp)":[26],"arrangement":[27],"$\\lceil":[29],"p^{3}/2\\rceil$":[30],"spheres.":[31],"For":[32],"this":[33,61],"family":[34],"packings,":[36,83],"previous":[38],"best-known":[39],"arrangements":[40,67],"were":[41],"usually":[42],"derived":[43],"from":[44],"ccp":[46],"by":[47],"omission":[48],"certain":[51],"without":[55],"changing":[56],"initial":[58],"structure.":[59],"In":[60],"paper,":[62],"we":[63],"show":[64],"that":[65],"better":[66],"exist":[68],"for":[69,89],"all":[70],"$n\\leq\\lceil":[71],"p^{3}/2\\rceil-2$.":[72],"introduce":[74],"an":[75],"optimization":[76],"method":[77],"to":[78],"reveal":[79],"improvements":[80,88],"these":[82],"and":[84],"present":[85],"many":[86],"new":[87],"$n\\leq4629$.":[90]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}