{"id":"https://openalex.org/W3117795836","doi":"https://doi.org/10.1142/s021819672350008x","title":"Primitivity index bounds in free groups, and the second Chebyshev function","display_name":"Primitivity index bounds in free groups, and the second Chebyshev function","publication_year":2022,"publication_date":"2022-11-21","ids":{"openalex":"https://openalex.org/W3117795836","doi":"https://doi.org/10.1142/s021819672350008x","mag":"3117795836"},"language":"en","primary_location":{"id":"doi:10.1142/s021819672350008x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672350008x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5023281472","display_name":"Ilya Kapovich","orcid":"https://orcid.org/0000-0002-7694-6236"},"institutions":[{"id":"https://openalex.org/I39694355","display_name":"Hunter College","ror":"https://ror.org/00g2xk477","country_code":"US","type":"education","lineage":["https://openalex.org/I39694355"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ilya Kapovich","raw_affiliation_strings":["Department of Mathematics and Statistics, Hunter College of CUNY, 695 Park Ave, New York, NY 10065, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Hunter College of CUNY, 695 Park Ave, New York, NY 10065, USA","institution_ids":["https://openalex.org/I39694355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019536704","display_name":"Zachary Simon","orcid":null},"institutions":[{"id":"https://openalex.org/I1287521167","display_name":"Lockheed Martin (United States)","ror":"https://ror.org/026er9r08","country_code":"US","type":"company","lineage":["https://openalex.org/I1287521167"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zachary Simon","raw_affiliation_strings":["Advanced Technology Center, Lockheed Martin Space, 1111 Lockheed Martin Way, Sunnyvale, CA 94089, USA"],"affiliations":[{"raw_affiliation_string":"Advanced Technology Center, Lockheed Martin Space, 1111 Lockheed Martin Way, Sunnyvale, CA 94089, USA","institution_ids":["https://openalex.org/I1287521167"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023281472"],"corresponding_institution_ids":["https://openalex.org/I39694355"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03739401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"01","first_page":"105","last_page":"122"},"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":0.9990000128746033,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.8673177361488342},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5769197940826416},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.562042236328125},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5320642590522766},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4550015926361084},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.41328543424606323},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4110841155052185},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40236207842826843},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3285692036151886},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1266079843044281}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8673177361488342},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5769197940826416},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.562042236328125},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5320642590522766},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4550015926361084},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.41328543424606323},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4110841155052185},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40236207842826843},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3285692036151886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1266079843044281},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819672350008x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672350008x","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1480319329","https://openalex.org/W1531598719","https://openalex.org/W1652789087","https://openalex.org/W1974386361","https://openalex.org/W1996018185","https://openalex.org/W2000035907","https://openalex.org/W2010256004","https://openalex.org/W2039071938","https://openalex.org/W2044157369","https://openalex.org/W2050733003","https://openalex.org/W2051115580","https://openalex.org/W2054631814","https://openalex.org/W2058062156","https://openalex.org/W2065954935","https://openalex.org/W2092723624","https://openalex.org/W2148372793","https://openalex.org/W2153126460","https://openalex.org/W2153632678","https://openalex.org/W2165003413","https://openalex.org/W2205200405","https://openalex.org/W2279609405","https://openalex.org/W2315950575","https://openalex.org/W2593183794","https://openalex.org/W2963187691","https://openalex.org/W2963190841","https://openalex.org/W2963691338","https://openalex.org/W2963890337","https://openalex.org/W2963890797","https://openalex.org/W2964279036","https://openalex.org/W2986262373","https://openalex.org/W3099242518","https://openalex.org/W3102345637","https://openalex.org/W3104503604","https://openalex.org/W3105214337","https://openalex.org/W4240318886"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W1996614773","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W2184046398"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"results":[2],"about":[3],"\u201cuntangling\u201d":[4],"closed":[5],"curves":[6],"on":[7],"hyperbolic":[8],"surfaces,":[9],"Gupta":[10],"and":[11,16,28,36,40,75,105],"Kapovich":[12],"introduced":[13],"the":[14,51,54,111,117,129],"primitivity":[15],"simplicity":[17],"index":[18],"functions":[19],"for":[20,43,77,91],"finitely":[21],"generated":[22],"free":[23],"groups,":[24],"[Formula:":[25,29,33,56,60,78,83,93,98],"see":[26,30,34,57,61,79,84,94,99],"text]":[27,58],"text],":[31,35,80,95],"where":[32],"obtained":[37],"some":[38],"upper":[39],"lower":[41],"bounds":[42],"these":[44],"functions.":[45],"In":[46,101],"this":[47,71],"paper,":[48],"we":[49,68,81,88],"study":[50],"behavior":[52],"of":[53,113,116],"sequence":[55,72],"as":[59],"text].":[62,85,100],"Answering":[63],"a":[64,125],"question":[65],"from":[66],"[17],":[67],"prove":[69],"that":[70,76,90],"is":[73],"unbounded":[74],"have":[82],"By":[86],"contrast,":[87],"show":[89],"all":[92],"one":[96],"has":[97],"addition":[102],"to":[103,123],"topological":[104],"group-theoretic":[106],"arguments,":[107],"number-theoretic":[108],"considerations,":[109],"particularly":[110],"use":[112],"asymptotic":[114],"properties":[115],"second":[118],"Chebyshev":[119],"function,":[120],"turn":[121],"out":[122],"play":[124],"key":[126],"role":[127],"in":[128],"proofs.":[130]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
