{"id":"https://openalex.org/W2063818754","doi":"https://doi.org/10.1109/ismvl.2013.7","title":"A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones","display_name":"A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones","publication_year":2013,"publication_date":"2013-05-01","ids":{"openalex":"https://openalex.org/W2063818754","doi":"https://doi.org/10.1109/ismvl.2013.7","mag":"2063818754"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/ismvl.2013.7","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01183004/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066732273","display_name":"Miguel Couceiro","orcid":"https://orcid.org/0000-0003-2316-7623"},"institutions":[{"id":"https://openalex.org/I4210137929","display_name":"Lamsade","ror":"https://ror.org/03pnp1a74","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I4210137929","https://openalex.org/I4210159245","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Miguel Couceiro","raw_affiliation_strings":["Knowledge representation, reasonning","Laboratoire d'analyse et mod\u00e9lisation de syst\u00e8mes pour l'aide \u00e0 la d\u00e9cision"],"affiliations":[{"raw_affiliation_string":"Knowledge representation, reasonning","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'analyse et mod\u00e9lisation de syst\u00e8mes pour l'aide \u00e0 la d\u00e9cision","institution_ids":["https://openalex.org/I4210137929"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006700188","display_name":"Lucien Haddad","orcid":null},"institutions":[{"id":"https://openalex.org/I51768193","display_name":"Royal Military College of Canada","ror":"https://ror.org/04yr71909","country_code":"CA","type":"education","lineage":["https://openalex.org/I51768193"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lucien Haddad","raw_affiliation_strings":["Royal Military College of Canada"],"affiliations":[{"raw_affiliation_string":"Royal Military College of Canada","institution_ids":["https://openalex.org/I51768193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016608014","display_name":"Karsten Sch\u00f6lzel","orcid":"https://orcid.org/0000-0003-4041-4219"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]},{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU","MX"],"is_corresponding":false,"raw_author_name":"Karsten Sch\u00f6lzel","raw_affiliation_strings":["Mathematics Research Unit","Universit\u00e9 du Luxembourg"],"affiliations":[{"raw_affiliation_string":"Mathematics Research Unit","institution_ids":["https://openalex.org/I124618812"]},{"raw_affiliation_string":"Universit\u00e9 du Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070313202","display_name":"Tam\u00e1s Waldhauser","orcid":"https://orcid.org/0000-0003-0365-6497"},"institutions":[{"id":"https://openalex.org/I227486990","display_name":"University of Szeged","ror":"https://ror.org/01pnej532","country_code":"HU","type":"education","lineage":["https://openalex.org/I227486990"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Tamas Waldhauser","raw_affiliation_strings":["Bolyai Institute [Szeged]","University of Szeged [Szeged]"],"affiliations":[{"raw_affiliation_string":"Bolyai Institute [Szeged]","institution_ids":[]},{"raw_affiliation_string":"University of Szeged [Szeged]","institution_ids":["https://openalex.org/I227486990"]}]}],"institution_assertions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":12,"citation_normalized_percentile":{"value":0.956608,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":86,"max":87},"biblio":{"volume":null,"issue":null,"first_page":"123","last_page":"128"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9977,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9977,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9977,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9943,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.77944124},{"id":"https://openalex.org/keywords/clone","display_name":"clone (Java method)","score":0.7410415},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5774649}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.77944124},{"id":"https://openalex.org/C81089528","wikidata":"https://www.wikidata.org/wiki/Q5134986","display_name":"clone (Java method)","level":3,"score":0.7410415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.65385985},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5774649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.56500083},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.52347696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4562974},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41748393},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32489336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28649393},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16436067},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.097320646},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.09672749},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.07294473},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C552990157","wikidata":"https://www.wikidata.org/wiki/Q7430","display_name":"DNA","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/ismvl.2013.7","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.science/hal-01090640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01183004","pdf_url":"https://inria.hal.science/hal-01183004/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01090640","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01183004","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01183004/file/9998_2.pdf","pdf_url":"https://hal.inria.fr/hal-01183004/file/9998_2.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01183004/document","pdf_url":"https://hal.inria.fr/hal-01183004/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01183004","pdf_url":"https://inria.hal.science/hal-01183004/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":12,"referenced_works":["https://openalex.org/W1589711670","https://openalex.org/W1974637223","https://openalex.org/W1995554919","https://openalex.org/W2016286898","https://openalex.org/W2058313567","https://openalex.org/W2111161140","https://openalex.org/W2122077663","https://openalex.org/W2152810174","https://openalex.org/W2159340286","https://openalex.org/W2161027123","https://openalex.org/W2161335750","https://openalex.org/W2963646536"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2560253012","https://openalex.org/W24519920","https://openalex.org/W2412288087","https://openalex.org/W2377327490","https://openalex.org/W2141060200","https://openalex.org/W2087778462","https://openalex.org/W2055384243","https://openalex.org/W2002177687","https://openalex.org/W1524590520"],"abstract_inverted_index":{"The":[0],"following":[1,58],"natural":[2],"problem,":[3],"first":[4],"considered":[5],"by":[6,12],"D.":[7],"Lau,":[8],"has":[9],"been":[10],"tackled":[11],"several":[13],"authors":[14],"recently:":[15],"Let":[16],"C":[17,65],"be":[18],"a":[19],"total":[20,38,63],"clone":[21,64],"on":[22,35,66],"2":[23,36],":=":[24],"{0,":[25],"1}.":[26],"Describe":[27],"the":[28,57,68],"interval":[29],"I(C)":[30,70],"of":[31,75],"all":[32],"partial":[33],"clones":[34],"whose":[37],"component":[39],"is":[40,71],"C.":[41],"We":[42],"establish":[43],"some":[44],"results":[45],"in":[46],"this":[47],"direction":[48],"and":[49],"combine":[50],"them":[51],"with":[52],"previous":[53],"ones":[54],"to":[55],"show":[56],"dichotomy":[59],"result:":[60],"For":[61],"every":[62],"2,":[67],"set":[69],"either":[72],"finite":[73],"or":[74],"continuum":[76],"cardinality.":[77]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2063818754","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2024-12-27T13:14:32.163256","created_date":"2016-06-24"}