{"id":"https://openalex.org/W2796808726","doi":"https://doi.org/10.37236/8565","title":"Constructions of Maximum Few-Distance Sets in Euclidean Spaces","display_name":"Constructions of Maximum Few-Distance Sets in Euclidean Spaces","publication_year":2020,"publication_date":"2020-01-24","ids":{"openalex":"https://openalex.org/W2796808726","doi":"https://doi.org/10.37236/8565","mag":"2796808726"},"language":"en","primary_location":{"id":"doi:10.37236/8565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p23/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/v27i1p23/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073144098","display_name":"Ferenc Sz\u00f6ll\u0151si","orcid":"https://orcid.org/0000-0002-7792-1049"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Ferenc Sz\u00f6ll\u0151si","raw_affiliation_strings":["Aalto University"],"affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009643905","display_name":"Patric R. J. \u00d6sterg\u00e5rd","orcid":"https://orcid.org/0000-0003-0426-9771"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Patric R.J. \u00d6sterg\u00e5rd","raw_affiliation_strings":["Aalto University"],"affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073144098"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.8866,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68534383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9979000091552734,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.8587083220481873},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7453757524490356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6511892080307007},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.6206479072570801},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5804554224014282},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.49037718772888184},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.48458874225616455},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48254603147506714},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4534454941749573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39431166648864746},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13355940580368042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11337733268737793}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8587083220481873},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7453757524490356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6511892080307007},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.6206479072570801},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5804554224014282},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.49037718772888184},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.48458874225616455},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48254603147506714},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4534454941749573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39431166648864746},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13355940580368042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11337733268737793},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p23/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:1804.06040","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.06040","pdf_url":"https://arxiv.org/pdf/1804.06040","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:2796808726","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1804.06040.pdf","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.1804.06040","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.06040","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":"doi:10.37236/8565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p23/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":[{"id":"https://openalex.org/G3609107129","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G6539779646","display_name":null,"funder_award_id":"289002","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G8025910944","display_name":null,"funder_award_id":"#289002","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2796808726.pdf","grobid_xml":"https://content.openalex.org/works/W2796808726.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1543806621","https://openalex.org/W1585305433","https://openalex.org/W1620653847","https://openalex.org/W1664859111","https://openalex.org/W1798099068","https://openalex.org/W1974316204","https://openalex.org/W1990600049","https://openalex.org/W2020003328","https://openalex.org/W2021036646","https://openalex.org/W2038645106","https://openalex.org/W2046112356","https://openalex.org/W2048741530","https://openalex.org/W2067544741","https://openalex.org/W2101796151","https://openalex.org/W2144778768","https://openalex.org/W2626927815","https://openalex.org/W2733176766","https://openalex.org/W2946247071","https://openalex.org/W2962738276","https://openalex.org/W6603764266","https://openalex.org/W6628599566","https://openalex.org/W6785349376"],"related_works":["https://openalex.org/W2775622620","https://openalex.org/W1994332726","https://openalex.org/W2731509995","https://openalex.org/W2083563352","https://openalex.org/W2806393619","https://openalex.org/W2287214931","https://openalex.org/W2988936625","https://openalex.org/W2002852610","https://openalex.org/W2950927864","https://openalex.org/W2116950483","https://openalex.org/W2009060894","https://openalex.org/W2593798505","https://openalex.org/W2159234836","https://openalex.org/W2089388332","https://openalex.org/W2365549031","https://openalex.org/W3185850073","https://openalex.org/W1550662968","https://openalex.org/W2979341318","https://openalex.org/W2338088544","https://openalex.org/W2892231032"],"abstract_inverted_index":{"A":[0],"finite":[1],"set":[2,16,19],"of":[3,20,26,40,44,76],"vectors":[4],"$\\mathcal{X}$":[5,27],"in":[6,56,62,69,80],"the":[7,18,52,58,65,95],"$d$-dimensional":[8],"Euclidean":[9],"space":[10],"$\\mathbb{R}^d$":[11,81],"is":[12],"called":[13],"an":[14],"$s$-distance":[15,78],"if":[17],"mutual":[21],"distances":[22],"between":[23],"distinct":[24],"elements":[25],"has":[28],"cardinality":[29],"exactly":[30],"$s$.":[31],"In":[32],"this":[33],"paper":[34],"we":[35],"present":[36],"a":[37],"combined":[38],"approach":[39],"isomorph-free":[41],"exhaustive":[42],"generation":[43],"graphs":[45],"and":[46,64,85,88],"Gr\u00f6bner":[47],"basis":[48],"computation":[49],"to":[50],"classify":[51],"largest":[53,59,66],"$3$-distance":[54],"sets":[55,61,68,79],"$\\mathbb{R}^4$,":[57],"$4$-distance":[60],"$\\mathbb{R}^3$,":[63],"$6$-distance":[67],"$\\mathbb{R}^2$.":[70],"We":[71],"also":[72],"construct":[73],"new":[74],"examples":[75],"large":[77],"for":[82],"$d\\leq":[83],"8$":[84],"$s\\leq":[86],"6$,":[87],"independently":[89],"verify":[90],"several":[91],"earlier":[92],"results":[93],"from":[94],"literature.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}