{"id":"https://openalex.org/W2654957689","doi":"https://doi.org/10.23638/dmtcs-20-1-10","title":"On subtrees of the representation tree in rational base numeration systems","display_name":"On subtrees of the representation tree in rational base numeration systems","publication_year":2018,"publication_date":"2018-03-05","ids":{"openalex":"https://openalex.org/W2654957689","doi":"https://doi.org/10.23638/dmtcs-20-1-10","mag":"2654957689"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-20-1-10","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-1-10","pdf_url":"https://dmtcs.episciences.org/4331/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/4331/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067137356","display_name":"Shigeki Akiyama","orcid":"https://orcid.org/0000-0001-7549-6686"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shigeki Akiyama","raw_affiliation_strings":["University of Tsukuba, Ibaraki, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013208252","display_name":"Victor Marsault","orcid":"https://orcid.org/0000-0002-2325-6004"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victor Marsault","raw_affiliation_strings":["Math\u00e9matiques discr\u00e8tes, Codage et Cryptographie"],"raw_orcid":"https://orcid.org/0000-0002-2325-6004","affiliations":[{"raw_affiliation_string":"Math\u00e9matiques discr\u00e8tes, Codage et Cryptographie","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012023435","display_name":"Jacques Sakarovitch","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210165912","display_name":"Laboratoire Traitement et Communication de l\u2019Information","ror":"https://ror.org/057er4c39","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102","https://openalex.org/I4210165912"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jacques Sakarovitch","raw_affiliation_strings":["IRIF, CNRS/Paris Diderot University and LTCI, Telecom-ParisTech, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIF, CNRS/Paris Diderot University and LTCI, Telecom-ParisTech, France","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I4210165912","https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067137356"],"corresponding_institution_ids":["https://openalex.org/I146399215"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02211744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Vol. 20 no. 1","issue":"Analysis of Algorithms","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":0.9086999893188477,"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":0.9086999893188477,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.024800000712275505,"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/T10126","display_name":"Logic, programming, and type systems","score":0.009499999694526196,"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/base","display_name":"Base (topology)","score":0.5986923575401306},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5536400675773621},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4719513952732086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45881351828575134},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.423906534910202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3994654715061188},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33066028356552124},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27600932121276855}],"concepts":[{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5986923575401306},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5536400675773621},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4719513952732086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45881351828575134},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.423906534910202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3994654715061188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33066028356552124},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27600932121276855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.23638/dmtcs-20-1-10","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-1-10","pdf_url":"https://dmtcs.episciences.org/4331/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/010caacd-3685-4383-b1dd-f5e0c6254d80","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/010caacd-3685-4383-b1dd-f5e0c6254d80","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Akiyama, S, Marsault, V & Sakarovitch, J 2018, 'On subtrees of the representation tree in rational base numeration systems', Discrete Mathematics & Theoretical Computer Science, vol. 20, no. 1, 10. < https://dmtcs.episciences.org/4331 >","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:publications/010caacd-3685-4383-b1dd-f5e0c6254d80","is_oa":true,"landing_page_url":"https://dmtcs.episciences.org/4331","pdf_url":"https://www.pure.ed.ac.uk/ws/files/64223641/1706.08266v3.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Akiyama, S, Marsault, V & Sakarovitch, J 2018, 'On subtrees of the representation tree in rational base numeration systems', Discrete Mathematics & Theoretical Computer Science, vol. 20, no. 1, 10. < https://dmtcs.episciences.org/4331 >","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-02287876v1","is_oa":false,"landing_page_url":"https://telecom-paris.hal.science/hal-02287876","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics and Theoretical Computer Science, 2018, 20 (1), pp.1-33. &#x27E8;10.23638/DMTCS-20-1-10&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:7a1589ed08a648ebb7ed0497b036cb11","is_oa":true,"landing_page_url":"https://doaj.org/article/7a1589ed08a648ebb7ed0497b036cb11","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science, Vol Vol. 20 no. 1, Iss Analysis of Algorithms (2018)","raw_type":"article"},{"id":"pmh:oai:orbi.ulg.ac.be:2268/258747","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/258747","pdf_url":null,"source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics and Theoretical Computer Science, 20 (1) (2018)","raw_type":"peer reviewed"},{"id":"doi:10.48550/arxiv.1706.08266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1706.08266","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-20-1-10","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-1-10","pdf_url":"https://dmtcs.episciences.org/4331/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.6899999976158142}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320323329","display_name":"Universit\u00e9 de Li\u00e8ge","ror":"https://ror.org/00afp2z80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2654957689.pdf","grobid_xml":"https://content.openalex.org/works/W2654957689.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1539382740","https://openalex.org/W1584451387","https://openalex.org/W1586417893","https://openalex.org/W1883548310","https://openalex.org/W1990014377","https://openalex.org/W2124301002","https://openalex.org/W2155254221","https://openalex.org/W2345562577"],"related_works":["https://openalex.org/W1549289070","https://openalex.org/W2963339245","https://openalex.org/W2044809295","https://openalex.org/W2335699373","https://openalex.org/W3011320943","https://openalex.org/W2531592663","https://openalex.org/W2135173043","https://openalex.org/W4253321761","https://openalex.org/W1889934247","https://openalex.org/W2892095864"],"abstract_inverted_index":{"Every":[0],"rational":[1,6],"number":[2],"p/q":[3,211],"defines":[4],"a":[5,15,26,50,100,219,225,276,308],"base":[7,210],"numeration":[8],"system":[9],"in":[10,64,209],"which":[11],"every":[12],"integer":[13],"has":[14],"unique":[16],"finite":[17],"representation,":[18],"up":[19],"to":[20,28,218,261,286,305],"leading":[21],"zeroes.":[22],"This":[23,39],"work":[24],"is":[25,46,90,96,110,117,137,146,180,190,224,229,252,259,274,295,300],"contribution":[27],"the":[29,32,35,43,57,91,97,103,118,122,125,131,135,148,151,157,164,171,194,197,213,232,235,238,254,262,265,283],"study":[30,156,287],"of":[31,34,37,42,88,99,102,108,115,133,234,237,240,245,249,256,264,267,271,278,311],"set":[33,132,270,310],"representations":[36],"integers.":[38],"prefix-closed":[40],"subset":[41,277],"free":[44],"monoid":[45],"naturally":[47],"represented":[48],"as":[49,150,196,206],"highly":[51],"non-regular":[52],"tree.":[53],"Its":[54],"nodes":[55],"are":[56,69],"integers,":[58],"its":[59,67,79,288],"edges":[60],"bear":[61],"labels":[62,236],"taken":[63],"{0,1,...,p-1},":[65],"and":[66,124,176,258,280,307],"subtrees":[68],"all":[70,134,162,272],"distinct.":[71],"We":[72,291],"associate":[73],"with":[74,78,168,174],"each":[75],"subtree":[76,226],"(or":[77],"root":[80,228],"n)":[81],"three":[82],"infinite":[83,141,184,201],"words.":[84],"The":[85,105,113,247,269],"bottom":[86,165],"word":[87,94,107,166,202],"n":[89,109,116,163,257],"lexicographically":[92],"smallest":[93],"that":[95,130,159,178,293],"label":[98],"branch":[101],"subtree.":[104],"top":[106],"defined":[111],"similarly.":[112],"span-word":[114,266],"digitwise":[119],"difference":[120],"between":[121],"latter":[123],"former.":[126],"First,":[127],"we":[128,155,281],"show":[129,177,292],"span-words":[136],"accepted":[138],"by":[139,182],"an":[140,183,207,243,296],"automaton":[142],"whose":[143,187,227],"underlying":[144,188],"graph":[145,189],"essentially":[147,193],"same":[149,195],"tree":[152,198],"itself.":[153,199],"Second,":[154],"function":[158],"computes":[160],"for":[161],"associated":[167,173],"n+1":[169],"from":[170],"one":[172],"n,":[175,230],"it":[179,294],"realised":[181],"sequential":[185],"transducer":[186],"once":[191],"again":[192],"An":[200],"may":[203],"be":[204],"interpreted":[205],"expansion":[208],"after":[212],"radix":[214],"point,":[215],"hence":[216],"evaluated":[217],"real":[220],"number.":[221],"If":[222],"T":[223,241],"then":[231,275],"evaluations":[233],"branches":[239],"form":[242],"interval":[244,251,297],"$\\mathbb{R}$.":[246],"length":[248],"this":[250],"called":[253],"span":[255],"equal":[260,304],"evaluation":[263],"n.":[268],"spans":[273],"R":[279],"use":[282],"preceding":[284],"construction":[285],"topological":[289],"closure.":[290],"when":[298],"p":[299],"greater":[301],"than":[302],"or":[303],"2q-1,":[306],"Cantor":[309],"measure":[312],"zero":[313],"otherwise.":[314],"Comment:":[315],"33":[316],"pages":[317]},"counts_by_year":[],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2017-06-30T00:00:00"}
