{"id":"https://openalex.org/W2166565522","doi":"https://doi.org/10.2478/v10037-009-0028-4","title":"Dilworth's Decomposition Theorem for Posets","display_name":"Dilworth's Decomposition Theorem for Posets","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2166565522","doi":"https://doi.org/10.2478/v10037-009-0028-4","mag":"2166565522"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-009-0028-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-009-0028-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-009-0028-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-009-0028-4","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052948222","display_name":"Piotr Rudnicki","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Piotr Rudnicki","raw_affiliation_strings":["University of Alberta Edmonton, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta Edmonton, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052948222"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":0.7575,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70915603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.8995000123977661,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.8995000123977661,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.8737000226974487,"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/T12170","display_name":"History and Theory of Mathematics","score":0.8406000137329102,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/mathematics","display_name":"Mathematics","score":0.8116511106491089},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6148319840431213},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5304989814758301},{"id":"https://openalex.org/keywords/decomposition-theorem","display_name":"Decomposition theorem","score":0.41864120960235596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4165880084037781},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3321754038333893},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.312439501285553}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8116511106491089},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6148319840431213},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5304989814758301},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.41864120960235596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4165880084037781},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3321754038333893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.312439501285553},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10037-009-0028-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-009-0028-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-009-0028-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.178.8124","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.8124","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2009-17/pdf17-4/dilworth.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:5b8aafee299247489be81dceaf094ab5","is_oa":true,"landing_page_url":"https://doaj.org/article/5b8aafee299247489be81dceaf094ab5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 17, Iss 4, Pp 223-232 (2009)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3548","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3548","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-009-0028-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-009-0028-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-009-0028-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2166565522.pdf","grobid_xml":"https://content.openalex.org/works/W2166565522.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W192809544","https://openalex.org/W1483101703","https://openalex.org/W1487872891","https://openalex.org/W1543162038","https://openalex.org/W1573317636","https://openalex.org/W1890412369","https://openalex.org/W1970064177","https://openalex.org/W1989047664","https://openalex.org/W2044935944","https://openalex.org/W2096461767","https://openalex.org/W2105559527","https://openalex.org/W2112898323","https://openalex.org/W2115474581","https://openalex.org/W2119808799","https://openalex.org/W2137957995","https://openalex.org/W2138492341","https://openalex.org/W2150008620","https://openalex.org/W2150348213","https://openalex.org/W2155453192","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W2330868067","https://openalex.org/W4254807835","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W2066456778","https://openalex.org/W4243997912"],"abstract_inverted_index":{"Dilworth's":[0,81],"Decomposition":[1],"Theorem":[2],"for":[3,54],"PosetsThe":[4],"following":[5,72],"theorem":[6,53,82],"is":[7,32,36,62,91,104,150],"due":[8],"to":[9,153],"Dilworth":[10,77],"[8]:":[11],"Let":[12],"P":[13,31,35],"be":[14],"a":[15,85,92,117,120,130],"partially":[16],"ordered":[17],"set.":[18],"If":[19],"the":[20,37,51,67,73,109,155,170],"maximal":[21],"number":[22],"of":[23,30,39,50,69,76,80,94,100,122,132,141,157,162],"elements":[24,128],"in":[25,65],"an":[26,47,138],"independent":[27,96,139],"subset":[28],"(anti-chain)":[29],"k,":[33],"then":[34,63,151],"union":[38,93],"k":[40],"chains":[41],"(cliques).In":[42],"this":[43,101],"article":[44],"we":[45,107,165],"formalize":[46],"elegant":[48],"proof":[49,75,99,110],"above":[52],"finite":[55],"posets":[56,71],"by":[57,111],"Perles":[58],"[13].":[59],"The":[60,98],"result":[61,156],"used":[64,152],"proving":[66],"case":[68],"infinite":[70],"original":[74],"[8].A":[78],"dual":[79,102],"also":[83,116],"holds:":[84],"poset":[86,121],"with":[87],"maximum":[88],"clique":[89,131],"m":[90,95],"sets.":[97],"fact":[103],"considerably":[105],"easier;":[106],"follow":[108],"Mirsky":[112,114],"[11].":[113],"states":[115],"corollary":[118,149],"that":[119],"r":[123,134],"x":[124],"s":[125,143],"+":[126,135,144],"1":[127,136],"possesses":[129],"size":[133,142],"or":[137,146],"set":[140],"1,":[145],"both.":[147],"This":[148],"prove":[154],"Erd\u0151s":[158],"and":[159,168,174],"Szekeres":[160],"[9].Instead":[161],"using":[163],"posets,":[164],"drop":[166],"reflexivity":[167],"state":[169],"facts":[171],"about":[172],"anti-symmetric":[173],"transitive":[175],"relations.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}