{"id":"https://openalex.org/W4304842645","doi":"https://doi.org/10.5070/c62359178","title":"Labelled well-quasi-order for permutation classes","display_name":"Labelled well-quasi-order for permutation classes","publication_year":2022,"publication_date":"2022-10-12","ids":{"openalex":"https://openalex.org/W4304842645","doi":"https://doi.org/10.5070/c62359178"},"language":"en","primary_location":{"id":"doi:10.5070/c62359178","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62359178","pdf_url":"https://escholarship.org/content/qt8579b1dq/qt8579b1dq.pdf?t=rjo23z","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt8579b1dq/qt8579b1dq.pdf?t=rjo23z","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000016207","display_name":"Robert Brignall","orcid":"https://orcid.org/0000-0002-2769-4853"},"institutions":[{"id":"https://openalex.org/I204136569","display_name":"The Open University","ror":"https://ror.org/05mzfcs16","country_code":"GB","type":"education","lineage":["https://openalex.org/I204136569"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert Brignall","raw_affiliation_strings":["School of Mathematics and Statistics, The Open University, Milton Keynes, England, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The Open University, Milton Keynes, England, U.K","institution_ids":["https://openalex.org/I204136569"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026309695","display_name":"Vincent Vatter","orcid":"https://orcid.org/0000-0001-5713-4059"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vincent Vatter","raw_affiliation_strings":["Department of Mathematics, University of Florida, Gainesville, Florida, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, Gainesville, Florida, U.S.A","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3042,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.60707248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"2","issue":"3","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":0.9943000078201294,"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":0.9943000078201294,"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":0.9930999875068665,"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":0.9793999791145325,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7628540992736816},{"id":"https://openalex.org/keywords/permutation-graph","display_name":"Permutation graph","score":0.6968944668769836},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6659736037254333},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5530267953872681},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5062609910964966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4989020824432373},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.46965423226356506},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4656539559364319},{"id":"https://openalex.org/keywords/partial-permutation","display_name":"Partial permutation","score":0.4313053488731384},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.42465126514434814},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3283691704273224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3063233494758606},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.0951891839504242},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08469361066818237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08010965585708618},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05272728204727173}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7628540992736816},{"id":"https://openalex.org/C68965932","wikidata":"https://www.wikidata.org/wiki/Q7169369","display_name":"Permutation graph","level":3,"score":0.6968944668769836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6659736037254333},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5530267953872681},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5062609910964966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4989020824432373},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.46965423226356506},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4656539559364319},{"id":"https://openalex.org/C145633696","wikidata":"https://www.wikidata.org/wiki/Q1401935","display_name":"Partial permutation","level":4,"score":0.4313053488731384},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.42465126514434814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3283691704273224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3063233494758606},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.0951891839504242},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08469361066818237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08010965585708618},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05272728204727173},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"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:10.5070/c62359178","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62359178","pdf_url":"https://escholarship.org/content/qt8579b1dq/qt8579b1dq.pdf?t=rjo23z","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5070/c62359178","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c62359178","pdf_url":"https://escholarship.org/content/qt8579b1dq/qt8579b1dq.pdf?t=rjo23z","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4304842645.pdf","grobid_xml":"https://content.openalex.org/works/W4304842645.grobid-xml"},"referenced_works_count":100,"referenced_works":["https://openalex.org/W137664942","https://openalex.org/W296433066","https://openalex.org/W632348028","https://openalex.org/W758484163","https://openalex.org/W1496524398","https://openalex.org/W1496896096","https://openalex.org/W1505308503","https://openalex.org/W1519715486","https://openalex.org/W1574446493","https://openalex.org/W1579049696","https://openalex.org/W1600513108","https://openalex.org/W1680910658","https://openalex.org/W1763742076","https://openalex.org/W1781381483","https://openalex.org/W1807584188","https://openalex.org/W1851784041","https://openalex.org/W1925430667","https://openalex.org/W1965749827","https://openalex.org/W1968120658","https://openalex.org/W1972783806","https://openalex.org/W1974351233","https://openalex.org/W1977950997","https://openalex.org/W1981803420","https://openalex.org/W1988098280","https://openalex.org/W1988827593","https://openalex.org/W1993476439","https://openalex.org/W1994679724","https://openalex.org/W1996873316","https://openalex.org/W1997435682","https://openalex.org/W1997481241","https://openalex.org/W2000763343","https://openalex.org/W2005287322","https://openalex.org/W2007843697","https://openalex.org/W2008070577","https://openalex.org/W2017003650","https://openalex.org/W2017788080","https://openalex.org/W2020139369","https://openalex.org/W2023990208","https://openalex.org/W2031830176","https://openalex.org/W2052953762","https://openalex.org/W2057303484","https://openalex.org/W2070286422","https://openalex.org/W2071321409","https://openalex.org/W2075312254","https://openalex.org/W2076508310","https://openalex.org/W2077866342","https://openalex.org/W2079856162","https://openalex.org/W2083354900","https://openalex.org/W2092807942","https://openalex.org/W2110610939","https://openalex.org/W2110917011","https://openalex.org/W2112942248","https://openalex.org/W2116087731","https://openalex.org/W2122172628","https://openalex.org/W2134705851","https://openalex.org/W2151245892","https://openalex.org/W2152949584","https://openalex.org/W2160859989","https://openalex.org/W2161008715","https://openalex.org/W2163841074","https://openalex.org/W2164211169","https://openalex.org/W2167462019","https://openalex.org/W2167928772","https://openalex.org/W2222990103","https://openalex.org/W2229257002","https://openalex.org/W2314887497","https://openalex.org/W2316437449","https://openalex.org/W2316932045","https://openalex.org/W2320406859","https://openalex.org/W2339922093","https://openalex.org/W2422380476","https://openalex.org/W2587431574","https://openalex.org/W2593657431","https://openalex.org/W2697533926","https://openalex.org/W2754503178","https://openalex.org/W2762850984","https://openalex.org/W2767249719","https://openalex.org/W2798714101","https://openalex.org/W2912910446","https://openalex.org/W2914427938","https://openalex.org/W2963127579","https://openalex.org/W2963317073","https://openalex.org/W2963351378","https://openalex.org/W2963940845","https://openalex.org/W2963998142","https://openalex.org/W2964002820","https://openalex.org/W2964181817","https://openalex.org/W2964197345","https://openalex.org/W2994155334","https://openalex.org/W3101041804","https://openalex.org/W3178242102","https://openalex.org/W4225938654","https://openalex.org/W4236220564","https://openalex.org/W4239860664","https://openalex.org/W4240833632","https://openalex.org/W4244392140","https://openalex.org/W4288400169","https://openalex.org/W4293867390","https://openalex.org/W4299866835","https://openalex.org/W6959456255"],"related_works":["https://openalex.org/W2385551783","https://openalex.org/W2964309395","https://openalex.org/W4285292213","https://openalex.org/W2356795487","https://openalex.org/W2391050754","https://openalex.org/W2952662568","https://openalex.org/W2141765721","https://openalex.org/W2349665798","https://openalex.org/W3133549692","https://openalex.org/W2078652738"],"abstract_inverted_index":{"While":[0],"the":[1,11,21,51,57],"theory":[2],"of":[3,23],"labelled":[4,34,72,84],"well-quasi-order":[5,48,94],"has":[6,15],"received":[7],"significant":[8],"attention":[9],"in":[10,20,50],"graph":[12,58,80],"setting,":[13],"it":[14],"not":[16],"yet":[17],"been":[18],"considered":[19],"context":[22],"permutation":[24,52,69,92],"patterns.":[25],"We":[26],"initiate":[27],"this":[28],"study":[29],"here,":[30],"and":[31,45,75],"show":[32],"how":[33],"well":[35],"quasi":[36],"order":[37],"provides":[38],"a":[39,68],"lens":[40],"through":[41],"which":[42],"to":[43,56],"view":[44],"extend":[46],"previous":[47],"results":[49],"patterns":[53],"literature.":[54],"Connections":[55],"setting":[59],"are":[60],"emphasised":[61],"throughout.":[62],"In":[63],"particular,":[64],"we":[65],"establish":[66],"that":[67],"class":[70,81],"is":[71,82],"well-quasi-ordered":[73],"if":[74,77],"only":[76],"its":[78],"corresponding":[79],"also":[83],"well-quasi-ordered.Mathematics":[85],"Subject":[86],"Classifications:":[87],"05A05,":[88],"06A07Keywords:":[89],"Labelled":[90],"well-quasi-order,":[91],"patterns,":[93]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}