{"id":"https://openalex.org/W2743057666","doi":"https://doi.org/10.37236/8044","title":"On Almost-Equidistant Sets - II","display_name":"On Almost-Equidistant Sets - II","publication_year":2019,"publication_date":"2019-05-03","ids":{"openalex":"https://openalex.org/W2743057666","doi":"https://doi.org/10.37236/8044","mag":"2743057666"},"language":"en","primary_location":{"id":"doi:10.37236/8044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p14/7827","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/v26i2p14/7827","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051157220","display_name":"Alexandr Polyanskii","orcid":"https://orcid.org/0000-0003-2423-6416"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Alexandr Polyanskii","raw_affiliation_strings":["Moscow Institute of Physics and Technology\r\nInstitute for Information Transmission Problems RAS"],"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology\r\nInstitute for Information Transmission Problems RAS","institution_ids":["https://openalex.org/I4210107660","https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051157220"],"corresponding_institution_ids":["https://openalex.org/I153845743","https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00381679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"2","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":0.9990000128746033,"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":0.9990000128746033,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9980999827384949,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9937999844551086,"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/equidistant","display_name":"Equidistant","score":0.9922634959220886},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7465778589248657},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.741963267326355},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.653229296207428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.651595413684845},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.6114615201950073},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.46636685729026794},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3839322626590729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0707445740699768}],"concepts":[{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.9922634959220886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7465778589248657},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.741963267326355},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.653229296207428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.651595413684845},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.6114615201950073},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.46636685729026794},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3839322626590729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0707445740699768},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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":4,"locations":[{"id":"doi:10.37236/8044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p14/7827","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:1708.02039","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.02039","pdf_url":"https://arxiv.org/pdf/1708.02039","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:2743057666","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1708.02039.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.1708.02039","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1708.02039","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:10.37236/8044","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8044","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p14/7827","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":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2743057666.pdf","grobid_xml":"https://content.openalex.org/works/W2743057666.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W993814535","https://openalex.org/W1969872431","https://openalex.org/W1970136394","https://openalex.org/W2023172083","https://openalex.org/W2076977679","https://openalex.org/W2402422612","https://openalex.org/W2732225744","https://openalex.org/W2963817832","https://openalex.org/W3105800933","https://openalex.org/W6656176459"],"related_works":["https://openalex.org/W2998922089","https://openalex.org/W2732225744","https://openalex.org/W993814535","https://openalex.org/W2950884009","https://openalex.org/W2996092231","https://openalex.org/W47156886","https://openalex.org/W150122160","https://openalex.org/W3098301955","https://openalex.org/W2392318637","https://openalex.org/W2578095078","https://openalex.org/W3102922066","https://openalex.org/W2081439462","https://openalex.org/W2143565095","https://openalex.org/W1597717682","https://openalex.org/W2412178246","https://openalex.org/W2246359575","https://openalex.org/W3124527033","https://openalex.org/W2072869041","https://openalex.org/W2095413082","https://openalex.org/W2953833920"],"abstract_inverted_index":{"A":[0],"set":[1,41,63,117],"in":[2,14,65,71,118],"$\\mathbb":[3,66,119],"R^d$":[4,67,120],"is":[5,79,86],"called":[6],"almost-equidistant":[7,40,62,116],"if":[8,74,84],"for":[9],"any":[10],"three":[11],"distinct":[12],"points":[13,70],"the":[15,31,75,107],"set,":[16],"some":[17],"two":[18,72],"are":[19],"at":[20,53,80,95],"unit":[21],"distance":[22],"apart.":[23],"First,":[24],"we":[25,58,101],"give":[26],"a":[27,44,87,90,103],"short":[28],"proof":[29,105],"of":[30,33,47,77,89,93,106,109],"result":[32,108],"Bezdek":[34],"and":[35,112],"L\u00e1ngi":[36],"claiming":[37],"that":[38,60,114],"an":[39,61,115],"lying":[42],"on":[43],"$(d-1)$-dimensional":[45],"sphere":[46],"radius":[48,94],"$r$,":[49],"where":[50,98],"$r&lt;1/\\sqrt{2}$,":[51],"has":[52,68,121],"most":[54,81,96],"$2d+2$":[55],"points.":[56],"Second,":[57],"prove":[59],"$V$":[64,78,85],"$O(d)$":[69],"cases:":[73],"diameter":[76],"$1$":[82],"or":[83],"subset":[88],"$d$-dimensional":[91],"ball":[92],"$1/\\sqrt{2}+cd^{-2/3}$,":[97],"$c&lt;1/2$.":[99],"Also,":[100],"present":[102],"new":[104],"Kupavskii,":[110],"Mustafa":[111],"Swanepoel":[113],"$O(d^{4/3})$":[122],"elements.":[123]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
