{"id":"https://openalex.org/W1970184655","doi":"https://doi.org/10.1137/s089548019426348x","title":"Classifying Hyperplanes in Hypercubes","display_name":"Classifying Hyperplanes in Hypercubes","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W1970184655","doi":"https://doi.org/10.1137/s089548019426348x","mag":"1970184655"},"language":"en","primary_location":{"id":"doi:10.1137/s089548019426348x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089548019426348x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5091823049","display_name":"Oswin Aichholzer","orcid":"https://orcid.org/0000-0002-2364-0583"},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Oswin Aichholzer","raw_affiliation_strings":["Institute of Software Technology (7160)"],"affiliations":[{"raw_affiliation_string":"Institute of Software Technology (7160)","institution_ids":["https://openalex.org/I4210128818"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065108210","display_name":"Franz Aurenhammer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Franz Aurenhammer","raw_affiliation_strings":["Institute of Theoretical Computer Science (7080)"],"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Computer Science (7080)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091823049"],"corresponding_institution_ids":["https://openalex.org/I4210128818"],"apc_list":null,"apc_paid":null,"fwci":0.5316,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.70675565,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"2","first_page":"225","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9592000246047974,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11476","display_name":"Graph theory and applications","score":0.9372000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.9431736469268799},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.916878342628479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7406361103057861},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6758533716201782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4156426787376404}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.9431736469268799},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.916878342628479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7406361103057861},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6758533716201782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4156426787376404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s089548019426348x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089548019426348x","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W24307859","https://openalex.org/W249091067","https://openalex.org/W586972575","https://openalex.org/W593210121","https://openalex.org/W1527837582","https://openalex.org/W1553934527","https://openalex.org/W1594652978","https://openalex.org/W1662824729","https://openalex.org/W1976465342","https://openalex.org/W2006995129","https://openalex.org/W2061055380","https://openalex.org/W2063165065","https://openalex.org/W2098730982","https://openalex.org/W2130586999","https://openalex.org/W2261415748","https://openalex.org/W2313866021","https://openalex.org/W2314571435","https://openalex.org/W2785506964","https://openalex.org/W2996335208","https://openalex.org/W4230719014","https://openalex.org/W4236313099","https://openalex.org/W4251029875"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W4286907761","https://openalex.org/W4376167435","https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W2213934937","https://openalex.org/W3022636680"],"abstract_inverted_index":{"We":[0,10,61],"consider":[1],"hyperplanes":[2,13,34,74,84,104],"spanned":[3,83],"by":[4,14,19,30],"vertices":[5,24,51],"of":[6,21,48,72,81,94,116],"the":[7,22,41,45,49,69,91,114],"unit":[8],"d-cube.":[9],"classify":[11],"these":[12,65],"parallelism":[15],"to":[16,86],"coordinate":[17],"axes,":[18],"symmetry":[20],"d-cube":[23,42,50,58],"they":[25,52,54],"avoid,":[26],"as":[27,29],"well":[28],"so-called":[31],"hull-honesty.":[32],"(Hull-honest":[33],"are":[35],"those":[36],"whose":[37],"intersection":[38],"figure":[39],"with":[40,44],"coincides":[43],"convex":[46],"hull":[47],"contain;":[53],"do":[55],"not":[56],"cut":[57],"edges":[59],"properly.)":[60],"describe":[62],"relationships":[63],"between":[64],"classes":[66],"and":[67,112],"give":[68],"exact":[70],"number":[71],"hull-honest":[73],"in":[75],"general":[76,97],"dimensions.":[77],"An":[78],"experimental":[79],"enumeration":[80,98],"all":[82],"up":[85],"dimension":[87],"eight":[88],"showed":[89],"us":[90],"intrinsic":[92],"difficulty":[93],"developing":[95],"a":[96],"scheme.":[99],"Motivation":[100],"for":[101],"considering":[102],"such":[103],"stems":[105],"from":[106,109,113],"coding":[107],"theory,":[108],"linear":[110],"programming,":[111],"theory":[115],"machine":[117],"learning.":[118]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}