{"id":"https://openalex.org/W1819573862","doi":"https://doi.org/10.37236/2473","title":"The Maximal Number of Runs in Standard Sturmian Words","display_name":"The Maximal Number of Runs in Standard Sturmian Words","publication_year":2013,"publication_date":"2013-01-21","ids":{"openalex":"https://openalex.org/W1819573862","doi":"https://doi.org/10.37236/2473","mag":"1819573862"},"language":"en","primary_location":{"id":"doi:10.37236/2473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p13/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/v20i1p13/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055998116","display_name":"Pawe\u0142 Baturo","orcid":null},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]},{"id":"https://openalex.org/I4210152232","display_name":"Institute of Informatics of the Slovak Academy of Sciences","ror":"https://ror.org/04jgqpc26","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210152232"]}],"countries":["PL","SK"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Baturo","raw_affiliation_strings":["Faculty of Mathematics and Computer Science Nicolaus Copernicus University Institute of Informatics Warsaw University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science Nicolaus Copernicus University Institute of Informatics Warsaw University","institution_ids":["https://openalex.org/I3019271933","https://openalex.org/I4210152232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035532665","display_name":"Marcin Pi\u0105tkowski","orcid":"https://orcid.org/0000-0001-5636-9497"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marcin Pi\u0105tkowski","raw_affiliation_strings":["Nicolaus Copernicus University\r\nToru\u0144, Poland","Nicolaus Copernicus University#R##N#Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nicolaus Copernicus University\r\nToru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]},{"raw_affiliation_string":"Nicolaus Copernicus University#R##N#Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079957387","display_name":"Wojciech Rytter","orcid":"https://orcid.org/0000-0002-9162-6724"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Wojciech Rytter","raw_affiliation_strings":["Warsaw University, Warsaw, Poland\r\nNicolaus Copernicus University, Toru\u0144, Poland","Warsaw University, Warsaw, Poland#R##N#Nicolaus Copernicus University, Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Warsaw University, Warsaw, Poland\r\nNicolaus Copernicus University, Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]},{"raw_affiliation_string":"Warsaw University, Warsaw, Poland#R##N#Nicolaus Copernicus University, Toru\u0144, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3645,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61286531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","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":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/T11269","display_name":"Algorithms and Data Compression","score":0.9991999864578247,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9984999895095825,"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/mathematics","display_name":"Mathematics","score":0.8513171672821045},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7730134725570679},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6994904279708862},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6698119044303894},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6573313474655151},{"id":"https://openalex.org/keywords/repetition","display_name":"Repetition (rhetorical device)","score":0.6028459072113037},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5616921782493591},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47436365485191345},{"id":"https://openalex.org/keywords/integer-sequence","display_name":"Integer sequence","score":0.46332308650016785},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4206123948097229},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.24441847205162048},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11254578828811646},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09271940588951111}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8513171672821045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7730134725570679},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6994904279708862},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6698119044303894},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6573313474655151},{"id":"https://openalex.org/C2776141515","wikidata":"https://www.wikidata.org/wiki/Q1274479","display_name":"Repetition (rhetorical device)","level":2,"score":0.6028459072113037},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5616921782493591},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47436365485191345},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.46332308650016785},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4206123948097229},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.24441847205162048},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11254578828811646},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09271940588951111},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"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:10.37236/2473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p13/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"}],"best_oa_location":{"id":"doi:10.37236/2473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p13/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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1819573862.pdf","grobid_xml":"https://content.openalex.org/works/W1819573862.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W584208200","https://openalex.org/W1528544059","https://openalex.org/W1541612046","https://openalex.org/W1549299641","https://openalex.org/W1574143058","https://openalex.org/W1882010690","https://openalex.org/W1976204600","https://openalex.org/W1987261421","https://openalex.org/W2001140974","https://openalex.org/W2001438476","https://openalex.org/W2003022262","https://openalex.org/W2025012811","https://openalex.org/W2036162092","https://openalex.org/W2087738656","https://openalex.org/W2088672239","https://openalex.org/W2401070439","https://openalex.org/W2407199015","https://openalex.org/W3148882068","https://openalex.org/W4297576944","https://openalex.org/W6633028832","https://openalex.org/W6659477988","https://openalex.org/W6793474325"],"related_works":["https://openalex.org/W2982781090","https://openalex.org/W3205355178","https://openalex.org/W147178145","https://openalex.org/W2894446991","https://openalex.org/W132694310","https://openalex.org/W1492950380","https://openalex.org/W1270085542","https://openalex.org/W2302567324","https://openalex.org/W2126653925","https://openalex.org/W3139825253"],"abstract_inverted_index":{"We":[0,72],"investigate":[1],"some":[2],"repetition":[3,51],"problems":[4,52],"for":[5,61,77],"a":[6,68,111],"very":[7,20],"special":[8],"class":[9],"$\\mathcal{S}$":[10],"of":[11,25,27,32,42,65,87,108,123],"strings":[12],"called":[13],"the":[14,30,40,62,106,121],"standard":[15,69,112],"Sturmian":[16,113],"words,":[17],"which":[18],"have":[19],"compact":[21],"representations":[22],"in":[23,53,67,110,115],"terms":[24],"sequences":[26],"integers.":[28],"Usually":[29],"size":[31,41,122],"this":[33],"word":[34,70,114],"is":[35,59,83],"exponential":[36],"with":[37,50,118],"respect":[38,119],"to":[39,104,120],"its":[43,124],"integer":[44],"sequence,":[45],"hence":[46],"we":[47,101],"are":[48],"dealing":[49],"compressed":[54,125],"strings.":[55],"An":[56],"explicit":[57],"formula":[58],"given":[60],"number":[63,107],"$\\rho(w)$":[64],"runs":[66,109],"$w$.":[71],"show":[73,102],"that":[74,94],"$\\rho(w)/|w|\\le":[75],"4/5$":[76],"each":[78],"$w\\in":[79],"S$,":[80],"and":[81],"there":[82],"an":[84],"infinite":[85],"sequence":[86],"strictly":[88],"growing":[89],"words":[90],"$w_k\\in":[91],"{\\mathcal{S}}$":[92],"such":[93],"$\\lim_{k\\rightarrow":[95],"\\infty}":[96],"\\frac{\\rho(w_k)}{|w_k|}":[97],"=":[98],"\\frac{4}{5}$.":[99],"Moreover,":[100],"how":[103],"compute":[105],"linear":[116],"time":[117],"representation.":[126]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}