{"id":"https://openalex.org/W3163411452","doi":"https://doi.org/10.1007/s00453-022-00950-y","title":"Asymptotic Analysis of q-Recursive Sequences","display_name":"Asymptotic Analysis of q-Recursive Sequences","publication_year":2022,"publication_date":"2022-05-04","ids":{"openalex":"https://openalex.org/W3163411452","doi":"https://doi.org/10.1007/s00453-022-00950-y","mag":"3163411452","pmid":"https://pubmed.ncbi.nlm.nih.gov/35974975"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-022-00950-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00950-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00950-y.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00950-y.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/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":"Clemens Heuberger","raw_affiliation_strings":["Alpen-Adria-Universit\u00e4t Klagenfurt, Klagenfurt, Austria"],"affiliations":[{"raw_affiliation_string":"Alpen-Adria-Universit\u00e4t Klagenfurt, Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033085976","display_name":"Daniel Krenn","orcid":"https://orcid.org/0000-0001-8076-8535"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Daniel Krenn","raw_affiliation_strings":["Paris Lodron University of Salzburg, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"Paris Lodron University of Salzburg, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027421588","display_name":"Gabriel F. Lipnik","orcid":"https://orcid.org/0000-0002-4362-429X"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Gabriel F. Lipnik","raw_affiliation_strings":["Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033085976"],"corresponding_institution_ids":["https://openalex.org/I182212641"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.9012,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75676268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"9","first_page":"2480","last_page":"2532"},"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":0.9983000159263611,"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/T11130","display_name":"Coding theory and cryptography","score":0.9980000257492065,"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":0.6981059312820435},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6134523153305054},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.596017599105835},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5664359331130981},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.46083691716194153},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.4469194710254669},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.43967100977897644},{"id":"https://openalex.org/keywords/pascal","display_name":"Pascal (unit)","score":0.4237043857574463},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.4204733967781067},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41291943192481995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.360604465007782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15257054567337036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1459973156452179}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6981059312820435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6134523153305054},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.596017599105835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5664359331130981},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.46083691716194153},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.4469194710254669},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.43967100977897644},{"id":"https://openalex.org/C75608658","wikidata":"https://www.wikidata.org/wiki/Q44395","display_name":"Pascal (unit)","level":2,"score":0.4237043857574463},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4204733967781067},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41291943192481995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.360604465007782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15257054567337036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1459973156452179},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-022-00950-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00950-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00950-y.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},{"id":"pmid:35974975","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35974975","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":null},{"id":"pmh:oai:arXiv.org:2105.04334","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.04334","pdf_url":"https://arxiv.org/pdf/2105.04334","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":"pmh:oai:pubmedcentral.nih.gov:9374655","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9374655","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Algorithmica","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00453-022-00950-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00950-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00950-y.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1908121808","display_name":null,"funder_award_id":"P 28466","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4284455511","display_name":null,"funder_award_id":"P28466-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5224225218","display_name":null,"funder_award_id":"P 28466-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6196800289","display_name":null,"funder_award_id":"W 1230","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/F4320323345","display_name":"Universit\u00e4t Salzburg","ror":"https://ror.org/05gs8cd61"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3163411452.pdf","grobid_xml":"https://content.openalex.org/works/W3163411452.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W347217945","https://openalex.org/W1490427800","https://openalex.org/W1514324498","https://openalex.org/W1586417893","https://openalex.org/W1974316666","https://openalex.org/W2032326995","https://openalex.org/W2052840430","https://openalex.org/W2077567940","https://openalex.org/W2081456387","https://openalex.org/W2083770519","https://openalex.org/W2096361394","https://openalex.org/W2101596584","https://openalex.org/W2132962549","https://openalex.org/W2165135131","https://openalex.org/W2266295420","https://openalex.org/W2331927488","https://openalex.org/W2465744178","https://openalex.org/W2490650842","https://openalex.org/W2570053645","https://openalex.org/W2587059192","https://openalex.org/W2592757846","https://openalex.org/W2594479812","https://openalex.org/W2765457434","https://openalex.org/W2787344833","https://openalex.org/W2796933303","https://openalex.org/W2963118546","https://openalex.org/W2981743500","https://openalex.org/W3099473684","https://openalex.org/W4210391712","https://openalex.org/W4231199984","https://openalex.org/W4238159413","https://openalex.org/W4238257903","https://openalex.org/W4241654653","https://openalex.org/W4402633180"],"related_works":["https://openalex.org/W2358676352","https://openalex.org/W2527515328","https://openalex.org/W1578720482","https://openalex.org/W4386999793","https://openalex.org/W2233052981","https://openalex.org/W2018157348","https://openalex.org/W3166262075","https://openalex.org/W2472085391","https://openalex.org/W2117194025","https://openalex.org/W2755681511"],"abstract_inverted_index":{"For":[0,137],"an":[1],"integer":[2],"<mml:math":[3],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>q</mml:mi>":[4],"<mml:mo>\u2265</mml:mo>":[5],"<mml:mn>2</mml:mn></mml:mrow>":[6],"</mml:math>":[7],",":[8],"a":[9,61,90],"<i>q</i>-recursive":[10,29,48,83],"sequence":[11,49,66],"is":[12,41,44,50],"defined":[13],"by":[14,71],"recurrence":[15,77],"relations":[16],"on":[17,89,93],"subsequences":[18],"of":[19,24,37,55,64,97,112,120,130],"indices":[20],"modulo":[21],"some":[22,124],"powers":[23],"<i>q</i>.":[25],"In":[26],"this":[27],"article,":[28],"sequences":[30,84,102],"are":[31,85,103],"studied":[32,104],"and":[33,57,59],"the":[34,53,65,73,76,94,109,113,134,138],"asymptotic":[35,80,95,110],"behavior":[36,111],"their":[38],"summatory":[39,114],"functions":[40,115],"analyzed.":[42],"It":[43],"shown":[45],"that":[46,60],"every":[47],"<i>q</i>-regular":[51,98],"in":[52,105,123,133],"sense":[54],"Allouche":[56],"Shallit":[58],"<i>q</i>-linear":[62],"representation":[63],"can":[67],"be":[68],"computed":[69],"easily":[70],"using":[72],"coefficients":[74],"from":[75],"relations.":[78],"Detailed":[79],"results":[81],"for":[82],"then":[86],"obtained":[87],"based":[88],"general":[91],"result":[92],"analysis":[96,143],"sequences.":[99],"Three":[100],"particular":[101],"detail:":[106],"We":[107],"discuss":[108],"ofStern's":[116],"diatomic":[117],"sequence,the":[118],"number":[119,129],"non-zero":[121],"elements":[122],"generalized":[125],"Pascal's":[126],"triangle":[127],"andthe":[128],"unbordered":[131],"factors":[132],"Thue-Morse":[135],"sequence.":[136],"first":[139],"two":[140],"sequences,":[141],"our":[142],"even":[144],"leads":[145],"to":[146],"precise":[147],"formul\u00e6":[148],"without":[149],"error":[150],"terms.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2021-05-24T00:00:00"}