{"id":"https://openalex.org/W3029056935","doi":"https://doi.org/10.37236/9351","title":"A Note on the Hurwitz Action on Reflection Factorizations of Coxeter Elements in Complex Reflection Groups","display_name":"A Note on the Hurwitz Action on Reflection Factorizations of Coxeter Elements in Complex Reflection Groups","publication_year":2020,"publication_date":"2020-06-26","ids":{"openalex":"https://openalex.org/W3029056935","doi":"https://doi.org/10.37236/9351","mag":"3029056935"},"language":"en","primary_location":{"id":"doi:10.37236/9351","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9351","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p54/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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p54/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Joel Brewster Lewis","orcid":null},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joel Brewster Lewis","raw_affiliation_strings":["George Washington University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Washington University","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I193531525"],"apc_list":null,"apc_paid":null,"fwci":0.547,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.59913793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8695999979972839,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8695999979972839,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.05270000174641609,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.014499999582767487,"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/coxeter-group","display_name":"Coxeter group","score":0.9100000262260437},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.7742999792098999},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6815999746322632},{"id":"https://openalex.org/keywords/point-group","display_name":"Point group","score":0.51910001039505},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.5188000202178955},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5001000165939331}],"concepts":[{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.9100000262260437},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.7742999792098999},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6815999746322632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6546000242233276},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.51910001039505},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5188000202178955},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5152999758720398},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C2781458696","wikidata":"https://www.wikidata.org/wiki/Q7307244","display_name":"Reflection group","level":4,"score":0.3921999931335449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3481999933719635},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C140860697","wikidata":"https://www.wikidata.org/wiki/Q5179941","display_name":"Coxeter element","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C37486056","wikidata":"https://www.wikidata.org/wiki/Q5179939","display_name":"Coxeter complex","level":4,"score":0.27900001406669617},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.2587999999523163}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/9351","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9351","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p54/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"},{"id":"pmh:oai:arXiv.org:2001.08238","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.08238","pdf_url":"https://arxiv.org/pdf/2001.08238","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"doi:10.37236/9351","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9351","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p54/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/W3029056935.pdf","grobid_xml":"https://content.openalex.org/works/W3029056935.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,18],"Hurwitz":[4],"action":[5],"is":[6],"\"as":[7],"transitive":[8],"as":[9],"possible\"":[10],"on":[11],"reflection":[12,21],"factorizations":[13],"of":[14,26],"Coxeter":[15],"elements":[16],"in":[17],"well-generated":[19],"complex":[20],"groups":[22],"$G(d,1,n)$":[23],"(the":[24],"group":[25],"$d$-colored":[27],"permutations)":[28],"and":[29],"$G(d,d,n)$.":[30]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-06-05T00:00:00"}