{"id":"https://openalex.org/W3177476908","doi":"https://doi.org/10.1007/s12095-021-00507-w","title":"Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences","display_name":"Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences","publication_year":2021,"publication_date":"2021-07-07","ids":{"openalex":"https://openalex.org/W3177476908","doi":"https://doi.org/10.1007/s12095-021-00507-w","mag":"3177476908"},"language":"en","primary_location":{"id":"doi:10.1007/s12095-021-00507-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-021-00507-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-021-00507-w.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12095-021-00507-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103612042","display_name":"Damien Jamet","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Damien Jamet","raw_affiliation_strings":["LORIA, UMR 7503, Universit\u00e9 de Lorraine, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","LORIA, UMR 7503, Universit\u00e9 de Lorraine, Vand\u0153uvre-l\u00e8s-Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LORIA, UMR 7503, Universit\u00e9 de Lorraine, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838"]},{"raw_affiliation_string":"LORIA, UMR 7503, Universit\u00e9 de Lorraine, Vand\u0153uvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I4210121838"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002939340","display_name":"Pierre Popoli","orcid":"https://orcid.org/0000-0002-4243-9180"},"institutions":[{"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/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Popoli","raw_affiliation_strings":["Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-4243-9180","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039057576","display_name":"Thomas Stoll","orcid":"https://orcid.org/0000-0003-2558-7875"},"institutions":[{"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/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thomas Stoll","raw_affiliation_strings":["Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, F-54506, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine/CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vand\u0153uvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103612042"],"corresponding_institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.1399,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54631138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"5","first_page":"791","last_page":"814"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7154985070228577},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6677327156066895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5761234760284424},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5632219314575195},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5565019845962524},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5467383861541748},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5019538402557373},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.49719861149787903},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49660831689834595},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4692297875881195}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7154985070228577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6677327156066895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5761234760284424},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5632219314575195},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5565019845962524},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5467383861541748},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5019538402557373},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49719861149787903},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49660831689834595},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4692297875881195},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s12095-021-00507-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-021-00507-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-021-00507-w.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.09959","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.09959","pdf_url":"https://arxiv.org/pdf/2106.09959","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3177476908","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2106.09959.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-03283528v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03283528","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://link.springer.com/article/10.1007/s12095-021-00507-w","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2106.09959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2106.09959","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"}],"best_oa_location":{"id":"doi:10.1007/s12095-021-00507-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12095-021-00507-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12095-021-00507-w.pdf","source":{"id":"https://openalex.org/S129219326","display_name":"Cryptography and Communications","issn_l":"1936-2447","issn":["1936-2447","1936-2455"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cryptography and Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1272171789","display_name":null,"funder_award_id":"ANR-18-CE40-0018","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3067370187","display_name":null,"funder_award_id":"ANR-20-CE91-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6876561401","display_name":null,"funder_award_id":"ANR-18","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8254623148","display_name":null,"funder_award_id":"ANR-15-IDEX-04-LUE","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8918884702","display_name":null,"funder_award_id":"15-IDEX-04-LUE","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177476908.pdf","grobid_xml":"https://content.openalex.org/works/W3177476908.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1497399181","https://openalex.org/W1519692838","https://openalex.org/W1833843757","https://openalex.org/W1971057901","https://openalex.org/W1972770363","https://openalex.org/W1979902210","https://openalex.org/W2022304193","https://openalex.org/W2050368732","https://openalex.org/W2098263571","https://openalex.org/W2100580582","https://openalex.org/W2158323623","https://openalex.org/W2165820698","https://openalex.org/W2405321428","https://openalex.org/W2419676999","https://openalex.org/W2607615482","https://openalex.org/W2898526269","https://openalex.org/W2909309548","https://openalex.org/W2963427995","https://openalex.org/W2964018583","https://openalex.org/W2972635911","https://openalex.org/W3033043605","https://openalex.org/W3090185765","https://openalex.org/W3093641005","https://openalex.org/W3103347853","https://openalex.org/W3120380919","https://openalex.org/W3137198537","https://openalex.org/W3162399915","https://openalex.org/W4238159413","https://openalex.org/W4239691897"],"related_works":["https://openalex.org/W3182950696","https://openalex.org/W2982386563","https://openalex.org/W3126486020","https://openalex.org/W3162399915","https://openalex.org/W2176409128","https://openalex.org/W3197993857","https://openalex.org/W2083101910","https://openalex.org/W1975949749","https://openalex.org/W2256754784","https://openalex.org/W2061734895","https://openalex.org/W3011783788","https://openalex.org/W58369529","https://openalex.org/W3192081671","https://openalex.org/W2081208267","https://openalex.org/W124404839","https://openalex.org/W2898303471","https://openalex.org/W2142669834","https://openalex.org/W2051931634","https://openalex.org/W2279209752","https://openalex.org/W2743385598"],"abstract_inverted_index":{"Abstract":[0],"Automatic":[1],"sequences":[2,6,31,68],"are":[3,19,32,57,69],"not":[4,83],"suitable":[5],"for":[7,60,94],"cryptographic":[8],"applications":[9],"since":[10],"both":[11],"their":[12,16,22],"subword":[13],"complexity":[14,18,98],"and":[15,21],"expansion":[17],"small,":[20],"correlation":[23],"measure":[24],"of":[25,49,66,77,99,102,112,123],"order":[26,40,97,129],"2":[27],"is":[28,82,109],"large.":[29],"These":[30],"highly":[33],"predictable":[34],"despite":[35],"having":[36],"a":[37,74,78,91,113],"large":[38,127],"maximum":[39,96,128],"complexity.":[41],"However,":[42],"recent":[43],"results":[44],"show":[45],"that":[46,81,119],"polynomial":[47,121],"subsequences":[48,122],"automatic":[50,67],"sequences,":[51,71],"such":[52,131],"as":[53,132],"the":[54,95,100,120,133],"Thue\u2013Morse":[55,134],"sequence,":[56],"better":[58],"candidates":[59],"pseudorandom":[61],"sequences.":[62],"A":[63],"natural":[64],"generalization":[65],"morphic":[70,114],"given":[72],"by":[73],"fixed":[75],"point":[76],"prolongeable":[79],"morphism":[80],"necessarily":[84],"uniform.":[85],"In":[86],"this":[87,124],"paper":[88],"we":[89],"prove":[90,118],"lower":[92],"bound":[93],"sum":[101],"digits":[103],"function":[104],"in":[105],"Zeckendorf":[106],"base":[107],"which":[108],"an":[110],"example":[111],"sequence.":[115,135],"We":[116],"also":[117],"sequence":[125],"keep":[126],"complexity,":[130]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-29T09:16:38.111599","created_date":"2025-10-10T00:00:00"}
