{"id":"https://openalex.org/W1573517507","doi":"https://doi.org/10.37236/3068","title":"The Prime Stems of Rooted Circuits of Closure Spaces and Minimum Implicational Bases","display_name":"The Prime Stems of Rooted Circuits of Closure Spaces and Minimum Implicational Bases","publication_year":2013,"publication_date":"2013-01-29","ids":{"openalex":"https://openalex.org/W1573517507","doi":"https://doi.org/10.37236/3068","mag":"1573517507"},"language":"en","primary_location":{"id":"doi:10.37236/3068","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3068","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p22/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p22/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035156230","display_name":"Masataka Nakamura","orcid":"https://orcid.org/0000-0002-0439-5682"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masataka Nakamura","raw_affiliation_strings":["University of Tokyo","university of Tokyo;"],"affiliations":[{"raw_affiliation_string":"University of Tokyo","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"university of Tokyo;","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009741215","display_name":"Kenji Kashiwabara","orcid":null},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenji Kashiwabara","raw_affiliation_strings":["University of Tokyo","university of Tokyo;"],"affiliations":[{"raw_affiliation_string":"University of Tokyo","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"university of Tokyo;","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035156230"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":0.3178,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57959891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13127","display_name":"Biotin and Related Studies","score":0.8744999766349792,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13127","display_name":"Biotin and Related Studies","score":0.8744999766349792,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10379","display_name":"Cellular Mechanics and Interactions","score":0.7577000260353088,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11472","display_name":"Analytical Chemistry and Sensors","score":0.7300999760627747,"subfield":{"id":"https://openalex.org/subfields/1502","display_name":"Bioengineering"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8103797435760498},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.7020303606987},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6407800912857056},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6394110918045044},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5599422454833984},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48184192180633545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44698524475097656},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42963269352912903},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4160163402557373},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37633591890335083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14917173981666565},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.12728840112686157},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1256875991821289}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8103797435760498},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7020303606987},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6407800912857056},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6394110918045044},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5599422454833984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48184192180633545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44698524475097656},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42963269352912903},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4160163402557373},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37633591890335083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14917173981666565},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.12728840112686157},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1256875991821289},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3068","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3068","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p22/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3068","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3068","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p22/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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1573517507.pdf","grobid_xml":"https://content.openalex.org/works/W1573517507.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1527517713","https://openalex.org/W1555123016","https://openalex.org/W2012644520","https://openalex.org/W2018498959","https://openalex.org/W2047348140","https://openalex.org/W2072284346","https://openalex.org/W2072414537","https://openalex.org/W2234563984","https://openalex.org/W2313098266","https://openalex.org/W4255318870","https://openalex.org/W6721604630","https://openalex.org/W6738730449","https://openalex.org/W6831631521"],"related_works":["https://openalex.org/W315394019","https://openalex.org/W2923398117","https://openalex.org/W4309585848","https://openalex.org/W2265383332","https://openalex.org/W4328130279","https://openalex.org/W4313657047","https://openalex.org/W2002342158","https://openalex.org/W2105009749","https://openalex.org/W4299387245","https://openalex.org/W4293797662"],"abstract_inverted_index":{"A":[0,21,123],"rooted":[1,22,125,133,144,156],"circuit":[2,23,134],"is":[3,24,66,127,172],"firstly":[4],"introduced":[5],"for":[6,13,18,136],"convex":[7,105],"geometries":[8],"(antimatroids).":[9],"We":[10,47],"generalize":[11],"it":[12],"closure":[14,19],"systems":[15],"or":[16],"equivalently":[17],"operators.":[20],"a":[25,29,33,37,45,49,52,70,97,111,128,132,140],"specific":[26],"type":[27],"of":[28,32,73,80,131],"pair":[30],"$(X,e)$":[31],"subset":[34],"$X$,":[35],"called":[36,44,51],"stem,":[38],"and":[39,92,115,148],"an":[40,74,103,120,137,152,168,175],"element":[41],"$e\\not\\in":[42],"X$,":[43],"root.":[46],"introduce":[48],"notion":[50],"'prime":[53],"stem',":[54],"which":[55],"plays":[56],"the":[57,78,84,86,107,164],"key":[58],"role":[59],"in":[60],"this":[61],"article.":[62],"Every":[63],"prime":[64,108],"stem":[65],"shown":[67,173],"to":[68,96,119,150,162],"be":[69],"pseudo-closed":[71,90],"set":[72],"implicational":[75,100,169],"system.":[76,170],"If":[77],"sizes":[79],"stems":[81,87,109],"are":[82,88,146,158],"all":[83,89],"same,":[85],"sets,":[91],"they":[93],"give":[94],"rise":[95,118],"canonical":[98,112],"minimum":[99,113],"basis.":[101,122],"For":[102],"affine":[104],"geometry,":[106],"determine":[110],"basis,":[114],"furthermore":[116],"gives":[117],"optimal":[121],"'critical":[124,143],"circuit'":[126],"special":[129],"case":[130],"defined":[135],"antimatroid.":[138],"As":[139],"precedence":[141],"structure,":[142],"circuits'":[145],"necessary":[147],"sufficient":[149,161],"fix":[151],"antimatroid":[153,166],"whereas":[154],"critical":[155],"circuits":[157],"not":[159],"necessarily":[160],"restore":[163],"original":[165],"as":[167],"It":[171],"through":[174],"example.":[176]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}