{"id":"https://openalex.org/W2037708290","doi":"https://doi.org/10.1142/s0218196708004469","title":"POSET REPRESENTATIONS OF DISTRIBUTIVE SEMILATTICES","display_name":"POSET REPRESENTATIONS OF DISTRIBUTIVE SEMILATTICES","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2037708290","doi":"https://doi.org/10.1142/s0218196708004469","mag":"2037708290"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004469","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004469","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0601058","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073101686","display_name":"Friedrich Wehrung","orcid":"https://orcid.org/0000-0002-4868-606X"},"institutions":[{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"FRIEDRICH WEHRUNG","raw_affiliation_strings":["CNR, UMR 6139, D\u00e9partement de Math\u00e9matiques, BP 5186, Universit\u00e9 de Caen, Campus 2, 14032 Caen Cedex, France"],"affiliations":[{"raw_affiliation_string":"CNR, UMR 6139, D\u00e9partement de Math\u00e9matiques, BP 5186, Universit\u00e9 de Caen, Campus 2, 14032 Caen Cedex, France","institution_ids":["https://openalex.org/I98702875"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073101686"],"corresponding_institution_ids":["https://openalex.org/I98702875"],"apc_list":null,"apc_paid":null,"fwci":0.411,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67077981,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"02","first_page":"321","last_page":"356"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","score":0.9939000010490417,"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/semilattice","display_name":"Semilattice","score":0.958219587802887},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7713295221328735},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.7277829647064209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7160731554031372},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6362919807434082},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.5533977746963501},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46773606538772583},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.44602951407432556},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.42717456817626953},{"id":"https://openalex.org/keywords/distributivity","display_name":"Distributivity","score":0.41783440113067627},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4161326289176941},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22202235460281372},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1265064775943756},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08615502715110779},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05167335271835327}],"concepts":[{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.958219587802887},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7713295221328735},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.7277829647064209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7160731554031372},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6362919807434082},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.5533977746963501},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46773606538772583},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.44602951407432556},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42717456817626953},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.41783440113067627},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4161326289176941},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22202235460281372},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1265064775943756},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08615502715110779},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05167335271835327},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1142/s0218196708004469","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004469","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0601058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0601058","pdf_url":"https://arxiv.org/pdf/math/0601058","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.2672","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.2672","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://fr.arxiv.org/pdf/math/0601058v3/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.9420","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.9420","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601058v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.7409","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.7409","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601058v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.8622","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.8622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0601058v2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00016421v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00016421","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":false,"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":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Algebra and Computation, 2008, 18 (2), pp.321--356. ⟨10.1142/S0218196708004469⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0601058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0601058","pdf_url":"https://arxiv.org/pdf/math/0601058","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W105902186","https://openalex.org/W1500907847","https://openalex.org/W1615794678","https://openalex.org/W1964694036","https://openalex.org/W1976989419","https://openalex.org/W1995418068","https://openalex.org/W1998153618","https://openalex.org/W2007208257","https://openalex.org/W2009622532","https://openalex.org/W2013060726","https://openalex.org/W2031228791","https://openalex.org/W2039062328","https://openalex.org/W2043634594","https://openalex.org/W2075430789","https://openalex.org/W2087612636","https://openalex.org/W2087625521","https://openalex.org/W2098879606","https://openalex.org/W2281874727","https://openalex.org/W2316021363","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2330170983","https://openalex.org/W2389398758","https://openalex.org/W433871523","https://openalex.org/W755468446","https://openalex.org/W2381226129","https://openalex.org/W2313033594","https://openalex.org/W2019118526","https://openalex.org/W1720430821","https://openalex.org/W2351462424","https://openalex.org/W2887793348"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,25,36,57,113],"for":[3,40,61,134],"every":[4,152],"distributive":[5,180],"\u3008\u2228,0\u3009-semilattice":[6],"S,":[7,81],"there":[8,89],"are":[9,90],"a":[10,16,85,91,96,124,159],"meet-semilattice":[11],"P":[12,19,21,75,157,162],"with":[13,48],"zero":[14],"and":[15,31,76,95,161],"map":[17],"\u03bc:":[18],"\u00d7":[20],"\u2192":[22],"S":[23,167],"such":[24,112],"\u03bc(x,z)":[26],"\u2264":[27,33,64,72,84,102,105,107,123,132],"\u03bc(x,y)":[28,37],"\u2228":[29,86],"\u03bc(y,z)":[30],"x":[32,100,103,108,120,129,144],"y":[34],"implies":[35,56],"=":[38,54,59,99,110],"0,":[39],"all":[41,62,70,77],"x,":[42],"y,":[43],"z":[44],"\u2208":[45,80,145],"P,":[46],"together":[47],"the":[49,148,171],"following":[50],"conditions:.":[51],"(P1)":[52],"\u03bc(v,u)":[53,83],"0":[55,101],"u":[58,63,71,98],"v,":[60],"v":[65,73,111],"in":[66,74,165],"P.":[67],"(P2)":[68],"For":[69],"a,":[78],"b":[79],"if":[82],"b,":[87,133],"then":[88],"positive":[92],"integer":[93],"n":[94,109],"decomposition":[97],"1":[104,118],"\u22ef":[106],"either":[114],"\u03bc(x":[115,126],"i":[116,121,130,136],"+":[117],",":[119,128],")":[122,131],"or":[125],"i+1":[127],"each":[135],"<":[137],"n.":[138],"(P3)":[139],"The":[140],"subset":[141,155],"{\u03bc(x,0)":[142],"|":[143],"P}":[146],"generates":[147],"semilattice":[149],"S.":[150],"Furthermore,":[151,170],"finite,":[153],"bounded":[154,164],"of":[156,178],"has":[158],"join,":[160],"is":[163,168,173],"case":[166],"bounded.":[169],"construction":[172],"functorial":[174],"on":[175],"lattice-indexed":[176],"diagrams":[177],"finite":[179],"\u3008\u2228,0,1\u3009-semilattices.":[181]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}