{"id":"https://openalex.org/W2134396130","doi":"https://doi.org/10.1080/10586458.2007.10129000","title":"The Minimum Dilatation of Pseudo-Anosov 5-Braids","display_name":"The Minimum Dilatation of Pseudo-Anosov 5-Braids","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2134396130","doi":"https://doi.org/10.1080/10586458.2007.10129000","mag":"2134396130"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2007.10129000","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129000","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089578612","display_name":"Ji-Young Ham","orcid":"https://orcid.org/0000-0001-8454-9647"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ji-Young Ham","raw_affiliation_strings":["Department of Mathematics, University of California Santa Barbara, CA 93106"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Santa Barbara, CA 93106","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027232852","display_name":"Won Taek Song","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Won Taek Song","raw_affiliation_strings":["School of Engineering, Information and Communications University, 119 Munjiro, Yuseong-gu, Daejeon 305-732, Korea"],"affiliations":[{"raw_affiliation_string":"School of Engineering, Information and Communications University, 119 Munjiro, Yuseong-gu, Daejeon 305-732, Korea","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089578612"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":4.8747,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.95519406,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"2","first_page":"167","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11567","display_name":"semigroups and automata theory","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"}}],"keywords":[{"id":"https://openalex.org/keywords/braid","display_name":"Braid","score":0.9513125419616699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9221288561820984},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5996612310409546},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4890500009059906},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3817463517189026},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32254141569137573},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.05337780714035034}],"concepts":[{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.9513125419616699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9221288561820984},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5996612310409546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4890500009059906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3817463517189026},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32254141569137573},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.05337780714035034},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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":4,"locations":[{"id":"doi:10.1080/10586458.2007.10129000","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2007.10129000","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.8986","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.8986","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/math/0506295v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.240.1417","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.1417","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/math/0506295v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.241.1872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.1872","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/math/0506295v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1595913392","https://openalex.org/W1964465325","https://openalex.org/W1965565198","https://openalex.org/W1982411021","https://openalex.org/W1994690121","https://openalex.org/W2003160845","https://openalex.org/W2034592120","https://openalex.org/W2035283484","https://openalex.org/W2040492196","https://openalex.org/W2046695973","https://openalex.org/W2051638203","https://openalex.org/W2059986855","https://openalex.org/W2065472085","https://openalex.org/W2068597507","https://openalex.org/W2070219994","https://openalex.org/W2071575743","https://openalex.org/W2073625014","https://openalex.org/W2076422355","https://openalex.org/W2081587878","https://openalex.org/W2089668258","https://openalex.org/W2119103923","https://openalex.org/W2153632678","https://openalex.org/W2171366636","https://openalex.org/W2802633207"],"related_works":["https://openalex.org/W1983695032","https://openalex.org/W1978622242","https://openalex.org/W3021719692","https://openalex.org/W3200673678","https://openalex.org/W4234871603","https://openalex.org/W2527628754","https://openalex.org/W2418687552","https://openalex.org/W3119071194","https://openalex.org/W2087757345","https://openalex.org/W2949959148"],"abstract_inverted_index":{"The":[0],"minimum":[1],"dilatation":[2],"of":[3,16],"pseudo-Anosov":[4],"5-braids":[5],"is":[6,25],"shown":[7],"to":[8],"be":[9],"the":[10],"largest":[11],"zero":[12],"\u03bb5":[13],"\u2248":[14],"1.72208":[15],"x":[17],"4":[18],"-x":[19,21],"3":[20],"2":[22],"-x+1,":[23],"which":[24],"attained":[26],"by":[27],"\u03c31\u03c32\u03c33\u03c34\u03c31\u03c32.":[28]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}