{"id":"https://openalex.org/W2237573901","doi":"https://doi.org/10.37236/5272","title":"Posets of Finite Functions","display_name":"Posets of Finite Functions","publication_year":2016,"publication_date":"2016-01-11","ids":{"openalex":"https://openalex.org/W2237573901","doi":"https://doi.org/10.37236/5272","mag":"2237573901"},"language":"en","primary_location":{"id":"doi:10.37236/5272","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5272","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v23i1p3/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011804577","display_name":"Konrad Pi\u00f3ro","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["CZ","PL"],"is_corresponding":true,"raw_author_name":"Konrad Pi\u00f3ro","raw_affiliation_strings":["Institute of Mathematics, University of Warsaw"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Warsaw","institution_ids":["https://openalex.org/I4654613","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011804577"],"corresponding_institution_ids":["https://openalex.org/I4210120266","https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01293502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.8947439789772034},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.8579025268554688},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7850787043571472},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7060892581939697},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.5800419449806213},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5382034778594971},{"id":"https://openalex.org/keywords/binary-operation","display_name":"Binary operation","score":0.4701801836490631},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.45949676632881165},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.4253942370414734},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35938501358032227}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8947439789772034},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.8579025268554688},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7850787043571472},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7060892581939697},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.5800419449806213},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5382034778594971},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.4701801836490631},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.45949676632881165},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.4253942370414734},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35938501358032227},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5272","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5272","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/5272","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5272","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p3/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2237573901.pdf","grobid_xml":"https://content.openalex.org/works/W2237573901.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W17345652","https://openalex.org/W112671161","https://openalex.org/W1500907847","https://openalex.org/W1509335165","https://openalex.org/W1516372139","https://openalex.org/W1986201476","https://openalex.org/W2014082748","https://openalex.org/W2023648368","https://openalex.org/W2093397547","https://openalex.org/W2164275177","https://openalex.org/W2758117960","https://openalex.org/W2914659449","https://openalex.org/W2993106468","https://openalex.org/W4205341637","https://openalex.org/W4232420208","https://openalex.org/W4293176479","https://openalex.org/W4300302225","https://openalex.org/W4300885858"],"related_works":["https://openalex.org/W4385431279","https://openalex.org/W4313071721","https://openalex.org/W2164275177","https://openalex.org/W2951380120","https://openalex.org/W4384652335","https://openalex.org/W2950832823","https://openalex.org/W1915796834","https://openalex.org/W3010829071","https://openalex.org/W4287827690","https://openalex.org/W2009663113"],"abstract_inverted_index":{"The":[0,51],"symmetric":[1],"group":[2],"$":[3,5,27,34,92,99,101,153,196],"S(n)":[4],"is":[6,14,43],"partially":[7],"ordered":[8],"by":[9,16,45,218,240],"Bruhat":[10],"order.":[11,167],"This":[12,41],"order":[13,74,147],"extended":[15],"L.":[17],"Renner":[18,73],"to":[19,100],"the":[20,55,150,164,172,192],"set":[21,151],"of":[22,26,54,57,81,124,133,152,171,175,191,194,212,228,232],"partial":[23,84,88],"injective":[24,86,89],"functions":[25,90,233],"\\{":[28,93,102],"1,":[29,94,103],"2,":[30,95,104],"\\ldots,":[31,96,105],"n":[32,97,154,197],"\\}":[33,98,107],"(see,":[35],"Linear":[36],"Algebraic":[37],"Monoids,":[38],"Springer,":[39],"2005).":[40],"poset":[42],"investigated":[44],"M.":[46],"Fortin":[47],"in":[48,149],"his":[49],"paper":[50,69],"MacNeille":[52],"Completion":[53],"Poset":[56],"Partial":[58],"Injective":[59],"Functions":[60],"[Electron.":[61],"J.":[62],"Combin.,":[63],"15,":[64],"R62,":[65],"2008].":[66],"In":[67,204],"this":[68],"we":[70,110,127,181,206],"show":[71,140],"that":[72,141],"can":[75,145],"be":[76,146],"also":[77,235],"defined":[78],"for":[79,187],"sets":[80],"all":[82,195],"functions,":[83,85],"and":[87,117,122,130,162,184,209,217,225],"from":[91],"m":[106,156,199],"$.":[108],"Next,":[109],"generalize":[111],"Fortin's":[112,136],"results":[113,220],"on":[114],"these":[115,142,213,241],"posets,":[116],"also,":[118],"using":[119],"simple":[120],"facts":[121],"methods":[123],"linear":[125],"algebra,":[126],"give":[128],"simpler":[129],"shorter":[131],"proofs":[132],"some":[134],"fundamental":[135],"results.":[137],"We":[138],"first":[139],"four":[143,230],"posets":[144,177,231],"embedded":[148],"\\times":[155,198],"$-matrices":[157,200],"with":[158,163,201],"non-negative":[159],"integer":[160,202],"entries":[161],"natural":[165],"componentwise":[166],"Second,":[168],"matrix":[169],"representations":[170],"Dedekind-MacNeille":[173,214,222],"completions":[174],"our":[176,229],"are":[178,234,244],"given.":[179],"Third,":[180],"find":[182],"join-":[183,208,224],"meet-irreducible":[185,210,226],"elements":[186,211,227,243],"every":[188],"finite":[189],"sublattice":[190],"lattice":[193],"entries.":[203],"particular,":[205],"obtain":[207],"completions.":[215],"Hence":[216],"general":[219],"concerning":[221],"completions,":[223],"found.":[236],"Moreover,":[237],"subposets":[238],"induced":[239],"irreducible":[242],"precisely":[245],"described.":[246]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}