{"id":"https://openalex.org/W2045359759","doi":"https://doi.org/10.1134/s0032946012020081","title":"Geometric relationship between parallel hyperplanes, quadrics, and vertices of a hypercube","display_name":"Geometric relationship between parallel hyperplanes, quadrics, and vertices of a hypercube","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W2045359759","doi":"https://doi.org/10.1134/s0032946012020081","mag":"2045359759"},"language":"en","primary_location":{"id":"doi:10.1134/s0032946012020081","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946012020081","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253","3034-5839"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-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":"https://openalex.org/A5021556310","display_name":"K. Yu. Gorbunov","orcid":"https://orcid.org/0000-0001-5438-6939"},"institutions":[{"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/I4210107660"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"K. Yu. Gorbunov","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050886196","display_name":"\u0410. \u0412. \u0421\u0435\u043b\u0438\u0432\u0435\u0440\u0441\u0442\u043e\u0432","orcid":"https://orcid.org/0000-0003-4746-6396"},"institutions":[{"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/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. V. Seliverstov","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076703141","display_name":"Vassily Lyubetsky","orcid":"https://orcid.org/0000-0002-3739-9161"},"institutions":[{"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/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. A. Lyubetsky","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia#TAB#","institution_ids":["https://openalex.org/I4210107660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021556310"],"corresponding_institution_ids":["https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":0.324,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61421514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"48","issue":"2","first_page":"185","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9736999869346619,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9736999869346619,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9689000248908997,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9645000100135803,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.9081051349639893},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8982604742050171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8301261067390442},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8073257207870483},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6246609687805176},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.6084720492362976},{"id":"https://openalex.org/keywords/unit-cube","display_name":"Unit cube","score":0.5263672471046448},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4626520574092865},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4321972727775574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41091740131378174},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09701874852180481}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.9081051349639893},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8982604742050171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8301261067390442},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8073257207870483},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6246609687805176},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.6084720492362976},{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.5263672471046448},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4626520574092865},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4321972727775574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41091740131378174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09701874852180481},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0032946012020081","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946012020081","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253","3034-5839"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W854929391","https://openalex.org/W1963547452","https://openalex.org/W1976465342","https://openalex.org/W1977277162","https://openalex.org/W2014485295","https://openalex.org/W2026891055","https://openalex.org/W2050336256","https://openalex.org/W2081024100","https://openalex.org/W2102204973","https://openalex.org/W2122595745","https://openalex.org/W2132788106","https://openalex.org/W2950641406","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W2213934937","https://openalex.org/W3022636680","https://openalex.org/W2135693030","https://openalex.org/W2157828285","https://openalex.org/W2361284192","https://openalex.org/W4250393251","https://openalex.org/W2031281829","https://openalex.org/W2164245886","https://openalex.org/W2120906584","https://openalex.org/W2113702600"],"abstract_inverted_index":{"In":[0],"a":[1,8,18,67,71,76,91,104,110],"space":[2],"of":[3,10,17,34,55,62,70,82,84,90,94,96,107,109],"dimension":[4,49],"30":[5],"we":[6],"find":[7],"pair":[9,102],"parallel":[11,97],"hyperplanes,":[12],"uniquely":[13],"determined":[14],"by":[15],"vertices":[16,33,61,83],"unit":[19],"cube":[20],"lying":[21],"on":[22,79],"them,":[23],"such":[24,99],"that":[25,100],"strictly":[26],"between":[27],"the":[28,35,63,80,85],"hyperplanes":[29,98],"there":[30,38],"are":[31,39],"no":[32],"cube,":[36,64],"though":[37],"integer":[40],"points.":[41],"A":[42],"similar":[43],"two-sided":[44],"example":[45],"is":[46,66],"constructed":[47],"in":[48],"37.":[50],"We":[51,87],"consider":[52],"possible":[53],"locations":[54],"empty":[56],"quadrics":[57],"with":[58],"respect":[59],"to":[60],"which":[65],"particular":[68],"case":[69],"discrete":[72],"optimization":[73],"problem":[74],"for":[75],"quadratic":[77],"polynomial":[78],"set":[81],"cube.":[86],"demonstrate":[88],"existence":[89],"large":[92,105],"number":[93,106],"pairs":[95],"each":[101],"contains":[103],"points":[108],"prescribed":[111],"set.":[112]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}