{"id":"https://openalex.org/W1640715524","doi":"https://doi.org/10.37236/5026","title":"Output Sum of Transducers: Limiting Distribution and Periodic Fluctuation","display_name":"Output Sum of Transducers: Limiting Distribution and Periodic Fluctuation","publication_year":2015,"publication_date":"2015-04-29","ids":{"openalex":"https://openalex.org/W1640715524","doi":"https://doi.org/10.37236/5026","mag":"1640715524"},"language":"en","primary_location":{"id":"doi:10.37236/5026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p19/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p19/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072500485","display_name":"Clemens Heuberger","orcid":"https://orcid.org/0000-0003-0082-7334"},"institutions":[{"id":"https://openalex.org/I134023368","display_name":"Institute for Interdisciplinary Studies of Austrian Universities","ror":"https://ror.org/001zf8v27","country_code":"AT","type":"education","lineage":["https://openalex.org/I134023368","https://openalex.org/I4210166741"]},{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Clemens Heuberger","raw_affiliation_strings":["Institut f\u00fcr Mathematik,\r\nAlpen-Adria-Universit\u00e4t Klagenfurt","Institut f\u00fcr Mathematik,#R##N#Alpen-Adria-Universit\u00e4t Klagenfurt"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik,\r\nAlpen-Adria-Universit\u00e4t Klagenfurt","institution_ids":["https://openalex.org/I4210166741"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik,#R##N#Alpen-Adria-Universit\u00e4t Klagenfurt","institution_ids":["https://openalex.org/I134023368"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003201046","display_name":"Sara Kropf","orcid":"https://orcid.org/0000-0002-1872-9567"},"institutions":[{"id":"https://openalex.org/I134023368","display_name":"Institute for Interdisciplinary Studies of Austrian Universities","ror":"https://ror.org/001zf8v27","country_code":"AT","type":"education","lineage":["https://openalex.org/I134023368","https://openalex.org/I4210166741"]},{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sara Kropf","raw_affiliation_strings":["Institut f\u00fcr Mathematik,\r\nAlpen-Adria-Universit\u00e4t Klagenfurt","Institut f\u00fcr Mathematik,#R##N#Alpen-Adria-Universit\u00e4t Klagenfurt"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik,\r\nAlpen-Adria-Universit\u00e4t Klagenfurt","institution_ids":["https://openalex.org/I4210166741"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik,#R##N#Alpen-Adria-Universit\u00e4t Klagenfurt","institution_ids":["https://openalex.org/I134023368"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014728682","display_name":"Helmut Prodinger","orcid":"https://orcid.org/0000-0002-0009-8015"},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Helmut Prodinger","raw_affiliation_strings":["Department of Mathematical Sciences,\r\nStellenbosch University","Department of Mathematical Sciences, Stellenbosch University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences,\r\nStellenbosch University","institution_ids":["https://openalex.org/I26092322"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Stellenbosch University","institution_ids":["https://openalex.org/I26092322"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072500485"],"corresponding_institution_ids":["https://openalex.org/I134023368","https://openalex.org/I4210166741"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.03582165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9991000294685364,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9991000294685364,"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/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"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":0.9976999759674072,"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/sequence","display_name":"Sequence (biology)","score":0.6955904960632324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6294249892234802},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5922912359237671},{"id":"https://openalex.org/keywords/periodic-sequence","display_name":"Periodic sequence","score":0.550327479839325},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5377377271652222},{"id":"https://openalex.org/keywords/transducer","display_name":"Transducer","score":0.5247895121574402},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5203932523727417},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5173922777175903},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.4540255665779114},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4516701400279999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3628600835800171},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36232975125312805},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36061108112335205},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17267277836799622},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16504305601119995}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6955904960632324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6294249892234802},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5922912359237671},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.550327479839325},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5377377271652222},{"id":"https://openalex.org/C56318395","wikidata":"https://www.wikidata.org/wiki/Q215928","display_name":"Transducer","level":2,"score":0.5247895121574402},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5203932523727417},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5173922777175903},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.4540255665779114},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4516701400279999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3628600835800171},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36232975125312805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36061108112335205},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17267277836799622},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16504305601119995},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/5026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p19/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1502.01412","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.01412","pdf_url":"https://arxiv.org/pdf/1502.01412","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":"doi:10.48550/arxiv.1502.01412","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1502.01412","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"},{"id":"mag:1640715524","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/5026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p19/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1625156126","display_name":"Asymptotic Analysis of Extremal Discrete Structures","funder_award_id":"P 24644","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3573016499","display_name":null,"funder_award_id":"P 24644-N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321697","display_name":"LOEWE Zentrum AdRIA","ror":"https://ror.org/05n911h24"},{"id":"https://openalex.org/F4320322663","display_name":"Universiteit Stellenbosch","ror":"https://ror.org/05bk57929"},{"id":"https://openalex.org/F4320325472","display_name":"Alpen-Adria-Universit\u00e4t Klagenfurt","ror":"https://ror.org/05q9m0937"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1640715524.pdf","grobid_xml":"https://content.openalex.org/works/W1640715524.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2238851036","https://openalex.org/W2488369978","https://openalex.org/W2615260901","https://openalex.org/W2890513793"],"related_works":["https://openalex.org/W2963561469","https://openalex.org/W2059508271","https://openalex.org/W2243404481","https://openalex.org/W2009318684","https://openalex.org/W2005248179","https://openalex.org/W2270686655","https://openalex.org/W2000700839","https://openalex.org/W1037205254","https://openalex.org/W2189112941","https://openalex.org/W2036688106","https://openalex.org/W322619368","https://openalex.org/W2964308758","https://openalex.org/W2055104190","https://openalex.org/W2016854575","https://openalex.org/W2004877571","https://openalex.org/W2064517065","https://openalex.org/W2950282806","https://openalex.org/W2126419612","https://openalex.org/W2559826918","https://openalex.org/W3099659626"],"abstract_inverted_index":{"As":[0,130],"a":[1,22,33,49],"generalization":[2],"of":[3,6,18,21,29,52,62,75,82,90,110,137],"the":[4,16,19,30,63,65,68,76,80,91,107,121,133,138],"sum":[5,17],"digits":[7],"function":[8,113,136],"and":[9,71,79,151],"other":[10],"digital":[11],"sequences,":[12],"sequences":[13],"defined":[14,47],"as":[15],"output":[20],"transducer":[23,31],"are":[24,43,85],"asymptotically":[25,124],"analyzed.":[26,142],"The":[27,87],"input":[28],"is":[32,94,114,123,141],"random":[34],"integer":[35],"in":[36,40,57,98],"$[0,":[37],"N)$.":[38],"Analogues":[39],"higher":[41],"dimensions":[42],"also":[44],"considered.":[45],"Sequences":[46],"by":[48,149],"certain":[50],"class":[51],"recursions":[53],"can":[54],"be":[55],"written":[56],"this":[58,83,111],"framework.Depending":[59],"on":[60],"properties":[61],"transducer,":[64],"main":[66],"term,":[67],"periodic":[69,88,112],"fluctuation":[70,89],"an":[72,131],"error":[73],"term":[74],"expected":[77,92],"value":[78,93],"variance":[81],"sequence":[84,122,140,144],"established.":[86],"H\u00f6lder":[95],"continuous":[96],"and,":[97],"many":[99,128],"cases,":[100],"nowhere":[101],"differentiable.":[102],"A":[103],"general":[104],"formula":[105],"for":[106,127],"Fourier":[108],"coefficients":[109],"derived.":[115],"Furthermore,":[116],"it":[117],"turns":[118],"out":[119],"that":[120],"normally":[125],"distributed":[126],"transducers.":[129],"example,":[132],"abelian":[134],"complexity":[135],"paperfolding":[139],"This":[143],"has":[145],"recently":[146],"been":[147],"studied":[148],"Madill":[150],"Rampersad.":[152]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}