{"id":"https://openalex.org/W1634002241","doi":"https://doi.org/10.37236/621","title":"Further Applications of a Power Series Method for Pattern Avoidance","display_name":"Further Applications of a Power Series Method for Pattern Avoidance","publication_year":2011,"publication_date":"2011-06-21","ids":{"openalex":"https://openalex.org/W1634002241","doi":"https://doi.org/10.37236/621","mag":"1634002241"},"language":"en","primary_location":{"id":"doi:10.37236/621","is_oa":true,"landing_page_url":"https://doi.org/10.37236/621","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p134/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":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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p134/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023519726","display_name":"Narad Rampersad","orcid":"https://orcid.org/0000-0001-7489-0980"},"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":"Narad Rampersad","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Winnipeg 515 Portage Avenue Winnipeg, Manitoba R3B 2E9 (Canada)","University of Winnipeg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Winnipeg 515 Portage Avenue Winnipeg, Manitoba R3B 2E9 (Canada)","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/A5023519726"],"corresponding_institution_ids":["https://openalex.org/I872945872"],"apc_list":null,"apc_paid":null,"fwci":2.2826,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.87054601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","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":1.0,"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":1.0,"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":0.9993000030517578,"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/T12029","display_name":"DNA and Biological Computing","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.8734288215637207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.850264310836792},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.785305380821228},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7845343351364136},{"id":"https://openalex.org/keywords/combinatorics-on-words","display_name":"Combinatorics on words","score":0.7808670401573181},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5624304413795471},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5522388219833374},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5367802977561951},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5117416381835938},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5096135139465332},{"id":"https://openalex.org/keywords/algebraic-combinatorics","display_name":"Algebraic combinatorics","score":0.4472367763519287},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44504687190055847},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.44096171855926514},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.4159855246543884},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.25943630933761597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05803456902503967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05139997601509094}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.8734288215637207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.850264310836792},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.785305380821228},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7845343351364136},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.7808670401573181},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5624304413795471},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5522388219833374},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5367802977561951},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5117416381835938},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5096135139465332},{"id":"https://openalex.org/C54643580","wikidata":"https://www.wikidata.org/wiki/Q1005603","display_name":"Algebraic combinatorics","level":2,"score":0.4472367763519287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44504687190055847},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44096171855926514},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.4159855246543884},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.25943630933761597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05803456902503967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05139997601509094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/621","is_oa":true,"landing_page_url":"https://doi.org/10.37236/621","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p134/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":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:CiteSeerX.psu:10.1.1.314.5785","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.5785","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/0907.4667v1.pdf","raw_type":"text"},{"id":"pmh:oai:winnspace.uwinnipeg.ca:10680/1413","is_oa":true,"landing_page_url":"http://hdl.handle.net/10680/1413","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.37236/621","is_oa":true,"landing_page_url":"https://doi.org/10.37236/621","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p134/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":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":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.5699999928474426}],"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/W1634002241.pdf","grobid_xml":"https://content.openalex.org/works/W1634002241.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W202791844","https://openalex.org/W600852147","https://openalex.org/W1586417893","https://openalex.org/W1969770235","https://openalex.org/W1972107895","https://openalex.org/W1973184666","https://openalex.org/W2012494262","https://openalex.org/W2017131087","https://openalex.org/W2024590752","https://openalex.org/W2030652989","https://openalex.org/W2039659422","https://openalex.org/W2060459509","https://openalex.org/W2086965829","https://openalex.org/W2405414321","https://openalex.org/W2911361414","https://openalex.org/W6642457312","https://openalex.org/W6643503482","https://openalex.org/W6654708597","https://openalex.org/W6656927846","https://openalex.org/W6658106452","https://openalex.org/W6660550348","https://openalex.org/W6672114803"],"related_works":["https://openalex.org/W3163303056","https://openalex.org/W4298247746","https://openalex.org/W2766493899","https://openalex.org/W2952831402","https://openalex.org/W2963534902","https://openalex.org/W2950489119","https://openalex.org/W2218762502","https://openalex.org/W2748444365","https://openalex.org/W4298306175","https://openalex.org/W1634002241"],"abstract_inverted_index":{"In":[0,90],"combinatorics":[1],"on":[2,107],"words,":[3],"a":[4,15,60,76],"word":[5],"$w$":[6,29],"over":[7,18,75],"an":[8,19,50,113],"alphabet":[9,20,78],"$\\Sigma$":[10],"is":[11,24,105],"said":[12],"to":[13,37,54,56,117],"avoid":[14,80],"pattern":[16,96],"$p$":[17,66],"$\\Delta$":[21],"if":[22],"there":[23,67],"no":[25,31],"factor":[26],"$x$":[27],"of":[28,64,72,87,100],"and":[30,45,119],"non-erasing":[32],"morphism":[33],"$h$":[34],"from":[35],"$\\Delta^*$":[36],"$\\Sigma^*$":[38],"such":[39],"that":[40,58,79,94],"$h(p)":[41],"=":[42],"x$.":[43],"Bell":[44],"Goh":[46],"have":[47],"recently":[48],"applied":[49],"algebraic":[51],"technique":[52],"due":[53,116],"Golod":[55],"show":[57,93],"for":[59],"certain":[61],"wide":[62],"class":[63],"patterns":[65],"are":[68],"exponentially":[69],"many":[70],"words":[71],"length":[73,101],"$n$":[74],"$4$-letter":[77],"$p$.":[81],"We":[82],"consider":[83],"some":[84],"further":[85],"consequences":[86],"their":[88],"work.":[89],"particular,":[91],"we":[92],"any":[95],"with":[97],"$k$":[98],"variables":[99],"at":[102],"least":[103],"$4^k$":[104],"avoidable":[106],"the":[108],"binary":[109],"alphabet.":[110],"This":[111],"improves":[112],"earlier":[114],"bound":[115],"Cassaigne":[118],"Roth.":[120]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}