{"id":"https://openalex.org/W2888684288","doi":"https://doi.org/10.1142/s0129054118420121","title":"One-Variable Word Equations and Three-Variable Constant-Free Word Equations","display_name":"One-Variable Word Equations and Three-Variable Constant-Free Word Equations","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2888684288","doi":"https://doi.org/10.1142/s0129054118420121","mag":"2888684288"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054118420121","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054118420121","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5077221909","display_name":"Dirk Nowotka","orcid":"https://orcid.org/0000-0002-5422-2229"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dirk Nowotka","raw_affiliation_strings":["Department of Computer Science, Kiel University, 24098 Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Kiel University, 24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031862611","display_name":"Aleksi Saarela","orcid":"https://orcid.org/0000-0002-6636-2317"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Aleksi Saarela","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077221909"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":null,"apc_paid":null,"fwci":0.8077,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.75280497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"05","first_page":"935","last_page":"950"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9958999752998352,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7968533039093018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7367814183235168},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.7206488251686096},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.703111469745636},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6433224678039551},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6102375388145447},{"id":"https://openalex.org/keywords/independent-equation","display_name":"Independent equation","score":0.44704440236091614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33703070878982544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2995716333389282},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.17199069261550903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11488792300224304},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08645600080490112}],"concepts":[{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7968533039093018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7367814183235168},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7206488251686096},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.703111469745636},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6433224678039551},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6102375388145447},{"id":"https://openalex.org/C200602138","wikidata":"https://www.wikidata.org/wiki/Q16979193","display_name":"Independent equation","level":3,"score":0.44704440236091614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33703070878982544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2995716333389282},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.17199069261550903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11488792300224304},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08645600080490112},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054118420121","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054118420121","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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":10,"referenced_works":["https://openalex.org/W1601888115","https://openalex.org/W1963886222","https://openalex.org/W1965895990","https://openalex.org/W2006565583","https://openalex.org/W2021028197","https://openalex.org/W2041189577","https://openalex.org/W2044452588","https://openalex.org/W2084952060","https://openalex.org/W2102446213","https://openalex.org/W2415254037"],"related_works":["https://openalex.org/W2110047855","https://openalex.org/W2142055042","https://openalex.org/W2977951435","https://openalex.org/W4293534416","https://openalex.org/W2490379986","https://openalex.org/W2022395185","https://openalex.org/W3119978365","https://openalex.org/W1992718970","https://openalex.org/W2888684288","https://openalex.org/W2043885859"],"abstract_inverted_index":{"We":[0,46,113],"prove":[1,16,114],"connections":[2],"between":[3],"one-variable":[4,67],"word":[5,10],"equations":[6,21,29,100],"and":[7,12],"three-variable":[8,27,98],"constant-free":[9,28,99],"equations,":[11],"use":[13],"them":[14],"to":[15,36],"that":[17,56,65,84,93,115],"the":[18,37,40,44,116,120],"number":[19],"of":[20,26,39,97,106],"in":[22,43],"an":[23],"independent":[24,95],"system":[25,96],"is":[30,58,86,105],"at":[31,75,108],"most":[32,76,109],"logarithmic":[33],"with":[34,101],"respect":[35],"length":[38],"shortest":[41],"equation":[42,68],"system.":[45],"also":[47],"study":[48],"two":[49],"well-known":[50],"conjectures.":[51],"The":[52,80],"first":[53,117],"conjecture":[54,82,118],"claims":[55,83],"there":[57,85],"a":[59,87,102,125],"constant":[60,88],"[Formula:":[61,77,89,110],"see":[62,78,90,111],"text]":[63,91],"such":[64,92],"every":[66,94],"has":[69],"either":[70],"infinitely":[71],"many":[72],"solutions":[73],"or":[74],"text].":[79,112],"second":[81,121],"nonperiodic":[103],"solution":[104],"size":[107],"implies":[119],"one,":[122],"possibly":[123],"for":[124],"different":[126],"constant.":[127]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}