{"id":"https://openalex.org/W1841290174","doi":"https://doi.org/10.37236/1215","title":"A note on antichains of words","display_name":"A note on antichains of words","publication_year":1995,"publication_date":"1995-10-14","ids":{"openalex":"https://openalex.org/W1841290174","doi":"https://doi.org/10.37236/1215","mag":"1841290174"},"language":"en","primary_location":{"id":"doi:10.37236/1215","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1215","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r21/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r21/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065770361","display_name":"James D. Currie","orcid":"https://orcid.org/0000-0002-0061-3849"},"institutions":[{"id":"https://openalex.org/I872945872","display_name":"University of Winnipeg","ror":"https://ror.org/02gdzyx04","country_code":"CA","type":"education","lineage":["https://openalex.org/I872945872"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"James D. Currie","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9","University of Winnipeg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9","institution_ids":["https://openalex.org/I872945872"]},{"raw_affiliation_string":"University of Winnipeg","institution_ids":["https://openalex.org/I872945872"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065770361"],"corresponding_institution_ids":["https://openalex.org/I872945872"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08679981,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","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":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","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/T11269","display_name":"Algorithms and Data Compression","score":0.9991000294685364,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9890000224113464,"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/antichain","display_name":"Antichain","score":0.9570844173431396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7738115191459656},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.7555230259895325},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7127875685691833},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6127808690071106},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4423779547214508},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43028175830841064},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.27115654945373535}],"concepts":[{"id":"https://openalex.org/C136134351","wikidata":"https://www.wikidata.org/wiki/Q431937","display_name":"Antichain","level":3,"score":0.9570844173431396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7738115191459656},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.7555230259895325},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7127875685691833},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6127808690071106},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4423779547214508},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43028175830841064},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.27115654945373535},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1215","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1215","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r21/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":false,"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"},{"id":"pmh:oai:winnspace.uwinnipeg.ca:10680/1349","is_oa":true,"landing_page_url":"http://hdl.handle.net/10680/1349","pdf_url":"http://hdl.handle.net/10680/1349","source":{"id":"https://openalex.org/S4306400200","display_name":"WinnSpace (University of Winnipeg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872945872","host_organization_name":"University of Winnipeg","host_organization_lineage":["https://openalex.org/I872945872"],"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":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.572","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.572","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.maths.tcd.ie/pub/EMIS/journals/EJC/Volume_2/PostScriptfiles/v2i1r21.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1215","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1215","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r21/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":false,"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":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1841290174.pdf","grobid_xml":"https://content.openalex.org/works/W1841290174.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W111211679","https://openalex.org/W1537696453","https://openalex.org/W1542999326","https://openalex.org/W1967905977","https://openalex.org/W1972107895","https://openalex.org/W1976016853","https://openalex.org/W1979656308","https://openalex.org/W1982787058","https://openalex.org/W2010717857","https://openalex.org/W2015129618","https://openalex.org/W2016879150","https://openalex.org/W2017131087","https://openalex.org/W2018977081","https://openalex.org/W2024590752","https://openalex.org/W2025237878","https://openalex.org/W2030652989","https://openalex.org/W2069902664","https://openalex.org/W2072919316","https://openalex.org/W2080123161","https://openalex.org/W2081579513","https://openalex.org/W2086965829","https://openalex.org/W2136069334","https://openalex.org/W2328110742","https://openalex.org/W3081952542","https://openalex.org/W4214859805","https://openalex.org/W4249162957"],"related_works":["https://openalex.org/W4246843255","https://openalex.org/W1519761499","https://openalex.org/W2047255619","https://openalex.org/W2022194745","https://openalex.org/W2065333210","https://openalex.org/W2003315074","https://openalex.org/W1925430667","https://openalex.org/W2097686156","https://openalex.org/W1654314556","https://openalex.org/W3041003668"],"abstract_inverted_index":{"We":[0,19,49],"can":[1],"compress":[2],"the":[3],"word":[4],"'banana'":[5,22],"as":[6],"$xyyz$,":[7],"where":[8],"$x":[9],"=$":[10],"'b',":[11],"$y":[12],"=":[13,16],"$":[14,17],"'an',$z":[15],"'a'.":[18],"say":[20],"that":[21,59],"encounters":[23,38],"$yy$.":[24],"Thus":[25],"a":[26],"'coded'":[27],"version":[28],"of":[29,68],"$yy$":[30],"shows":[31],"up":[32],"in":[33,60],"'banana'.":[34],"The":[35],"relation":[36],"'$u$":[37],"$w$'":[39],"is":[40,64],"transitive,":[41],"and":[42],"thus":[43],"generates":[44],"an":[45,65],"order":[46,62],"on":[47],"words.":[48],"study":[50],"antichains":[51],"under":[52],"this":[53,61],"order.":[54],"In":[55],"particular":[56],"we":[57],"show":[58],"there":[63],"infinite":[66],"antichain":[67],"binary":[69],"words":[70],"avoiding":[71],"overlaps.":[72]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}