{"id":"https://openalex.org/W2980005048","doi":"https://doi.org/10.1007/s00453-019-00623-3","title":"Analytic Combinatorics of Lattice Paths with Forbidden Patterns, the Vectorial Kernel Method, and Generating Functions for Pushdown Automata","display_name":"Analytic Combinatorics of Lattice Paths with Forbidden Patterns, the Vectorial Kernel Method, and Generating Functions for Pushdown Automata","publication_year":2019,"publication_date":"2019-10-13","ids":{"openalex":"https://openalex.org/W2980005048","doi":"https://doi.org/10.1007/s00453-019-00623-3","mag":"2980005048"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-019-00623-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00623-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00623-3.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":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00623-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048476389","display_name":"Andrei Asinowski","orcid":"https://orcid.org/0000-0002-0689-0775"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]},{"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":"Andrei Asinowski","raw_affiliation_strings":["Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Vienna, Austria","Institut f\u00fcr Mathematik, Alpen-Adria Universit\u00e4t Klagenfurt, Klagenfurt, Austria"],"raw_orcid":"https://orcid.org/0000-0002-0689-0775","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Alpen-Adria Universit\u00e4t Klagenfurt, Klagenfurt, Austria","institution_ids":["https://openalex.org/I4210166741"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102913488","display_name":"Axel Bacher","orcid":"https://orcid.org/0000-0002-9789-7074"},"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/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Axel Bacher","raw_affiliation_strings":["LIPN, UMR CNRS 7030, Universit\u00e9 Paris 13, Villetaneuse, France"],"raw_orcid":"https://orcid.org/0000-0002-9789-7074","affiliations":[{"raw_affiliation_string":"LIPN, UMR CNRS 7030, Universit\u00e9 Paris 13, Villetaneuse, France","institution_ids":["https://openalex.org/I4210156583","https://openalex.org/I1294671590","https://openalex.org/I4210091279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047713303","display_name":"Cyril Banderier","orcid":"https://orcid.org/0000-0003-0755-3022"},"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/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cyril Banderier","raw_affiliation_strings":["LIPN, UMR CNRS 7030, Universit\u00e9 Paris 13, Villetaneuse, France"],"raw_orcid":"https://orcid.org/0000-0003-0755-3022","affiliations":[{"raw_affiliation_string":"LIPN, UMR CNRS 7030, Universit\u00e9 Paris 13, Villetaneuse, France","institution_ids":["https://openalex.org/I4210156583","https://openalex.org/I1294671590","https://openalex.org/I4210091279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037333569","display_name":"Bernhard Gittenberger","orcid":"https://orcid.org/0000-0002-2639-8227"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Bernhard Gittenberger","raw_affiliation_strings":["Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2639-8227","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048476389"],"corresponding_institution_ids":["https://openalex.org/I145847075","https://openalex.org/I4210166741"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":6.5787,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.97894737,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"82","issue":"3","first_page":"386","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9990000128746033,"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":0.9743000268936157,"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/enumeration","display_name":"Enumeration","score":0.7706462144851685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7057943344116211},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6160077452659607},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5697362422943115},{"id":"https://openalex.org/keywords/pushdown-automaton","display_name":"Pushdown automaton","score":0.5171410441398621},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4799266457557678},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46409860253334045},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4610312283039093},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2798502445220947},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.2674522399902344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18360117077827454},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.11231034994125366}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7706462144851685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7057943344116211},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6160077452659607},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5697362422943115},{"id":"https://openalex.org/C77944639","wikidata":"https://www.wikidata.org/wiki/Q751443","display_name":"Pushdown automaton","level":3,"score":0.5171410441398621},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4799266457557678},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46409860253334045},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4610312283039093},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2798502445220947},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.2674522399902344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18360117077827454},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.11231034994125366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00453-019-00623-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00623-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00623-3.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":"pmh:oai:HAL:hal-02413650v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02413650","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":"Algorithmica, In press","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00453-019-00623-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-019-00623-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-019-00623-3.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/G1767973943","display_name":null,"funder_award_id":"SFB F50-03","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"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/G235251219","display_name":null,"funder_award_id":"(SFB F50-03)","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2549575712","display_name":null,"funder_award_id":"SFB F50","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/G8982020810","display_name":null,"funder_award_id":"(P 28466-N35)","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2980005048.pdf","grobid_xml":"https://content.openalex.org/works/W2980005048.grobid-xml"},"referenced_works_count":83,"referenced_works":["https://openalex.org/W70662222","https://openalex.org/W186403072","https://openalex.org/W589969373","https://openalex.org/W1485110504","https://openalex.org/W1490446672","https://openalex.org/W1543276479","https://openalex.org/W1558729961","https://openalex.org/W1562379951","https://openalex.org/W1563548847","https://openalex.org/W1611577713","https://openalex.org/W1727739892","https://openalex.org/W1843426194","https://openalex.org/W1890888469","https://openalex.org/W1906132287","https://openalex.org/W1951920023","https://openalex.org/W1966578568","https://openalex.org/W1977907530","https://openalex.org/W1981765142","https://openalex.org/W1982581840","https://openalex.org/W1985505035","https://openalex.org/W1999722679","https://openalex.org/W1999907474","https://openalex.org/W2002089154","https://openalex.org/W2003153172","https://openalex.org/W2010100934","https://openalex.org/W2012164137","https://openalex.org/W2014724230","https://openalex.org/W2015569722","https://openalex.org/W2020945831","https://openalex.org/W2028732503","https://openalex.org/W2033983166","https://openalex.org/W2034762331","https://openalex.org/W2035219093","https://openalex.org/W2040889864","https://openalex.org/W2044357323","https://openalex.org/W2045191540","https://openalex.org/W2065307651","https://openalex.org/W2067312426","https://openalex.org/W2068033911","https://openalex.org/W2068406291","https://openalex.org/W2072426462","https://openalex.org/W2074094847","https://openalex.org/W2083916911","https://openalex.org/W2086582845","https://openalex.org/W2091599083","https://openalex.org/W2093772480","https://openalex.org/W2095328322","https://openalex.org/W2097243530","https://openalex.org/W2109846666","https://openalex.org/W2117810714","https://openalex.org/W2121074682","https://openalex.org/W2122019510","https://openalex.org/W2130349753","https://openalex.org/W2138222708","https://openalex.org/W2140990372","https://openalex.org/W2144210409","https://openalex.org/W2175442372","https://openalex.org/W2271322173","https://openalex.org/W2340541605","https://openalex.org/W2399917757","https://openalex.org/W2412408975","https://openalex.org/W2538787759","https://openalex.org/W2793865282","https://openalex.org/W2911565153","https://openalex.org/W2918466505","https://openalex.org/W2962781158","https://openalex.org/W2963095869","https://openalex.org/W2963187226","https://openalex.org/W2963222432","https://openalex.org/W2963281515","https://openalex.org/W2963578516","https://openalex.org/W2964293977","https://openalex.org/W2969130840","https://openalex.org/W2989713547","https://openalex.org/W2993227039","https://openalex.org/W2999128257","https://openalex.org/W3015657067","https://openalex.org/W3101445366","https://openalex.org/W4241626994","https://openalex.org/W4243410516","https://openalex.org/W4244639301","https://openalex.org/W4285719527","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W157429075","https://openalex.org/W5819577","https://openalex.org/W2359831739"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,109,200],"article":[3],"we":[4,94,161,180],"develop":[5],"a":[6,16,30,44,56,128],"vectorial":[7],"kernel":[8],"method":[9,12],"\u2014a":[10],"powerful":[11],"which":[13],"solves":[14],"in":[15,72,118,120],"unified":[17],"framework":[18],"all":[19],"the":[20,24,37,53,79,105,121,141,154,164,175,183,195,198],"problems":[21],"related":[22],"to":[23,99,194],"enumeration":[25,38,88,142],"of":[26,39,55,91,108,123,143,146,157,172,174,185,197,209],"words":[27],"generated":[28],"by":[29,81,114],"pushdown":[31],"automaton.":[32],"We":[33,59,102],"apply":[34],"it":[35],"for":[36,51,131],"lattice":[40,92],"paths":[41],"that":[42,104,182],"avoid":[43],"fixed":[45],"word":[46],"(a":[47],"pattern":[48,176],"),":[49,178],"or":[50],"counting":[52],"occurrences":[54,173,186],"given":[57],"pattern.":[58],"unify":[60],"results":[61,98,139],"from":[62,85,153],"numerous":[63],"articles":[64],"concerning":[65],"patterns":[66],"like":[67],"peaks,":[68],"valleys,":[69],"humps,":[70],"etc.,":[71],"Dyck":[73],"and":[74,83,89,116,149,179,190,204],"Motzkin":[75],"paths.":[76],"This":[77],"refines":[78],"study":[80],"Banderier":[82],"Flajolet":[84,203],"2002":[86],"on":[87],"asymptotics":[90],"paths:":[93],"extend":[95],"here":[96],"their":[97],"pattern-avoiding":[100],"walks/bridges/meanders/excursions.":[101],"show":[103],"autocorrelation":[106],"polynomial":[107],"forbidden":[110],"pattern,":[111],"as":[112],"introduced":[113],"Guibas":[115],"Odlyzko":[117],"1981":[119],"context":[122],"rational":[124],"languages,":[125],"still":[126],"plays":[127],"crucial":[129],"role":[130],"our":[132,138],"algebraic":[133],"languages.":[134],"En":[135],"passant":[136],",":[137],"give":[140,163],"some":[144],"classes":[145],"self-avoiding":[147],"walks,":[148],"prove":[150,181],"several":[151],"conjectures":[152],"On-Line":[155],"Encyclopedia":[156],"Integer":[158],"Sequences.":[159],"Finally,":[160],"also":[162],"trivariate":[165],"generating":[166],"function":[167],"(length,":[168],"final":[169],"altitude,":[170],"number":[171,184],"p":[177],"is":[187,201],"normally":[188],"distributed":[189],"linear":[191],"with":[192],"respect":[193],"length":[196],"walk:":[199],"what":[202],"Sedgewick":[205],"call":[206],"an":[207],"instance":[208],"Borges\u2019s":[210],"theorem":[211],".":[212]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
