{"id":"https://openalex.org/W2070539158","doi":"https://doi.org/10.1145/2229163.2229175","title":"Counting occurrences for a finite set of words","display_name":"Counting occurrences for a finite set of words","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2070539158","doi":"https://doi.org/10.1145/2229163.2229175","mag":"2070539158"},"language":"en","primary_location":{"id":"doi:10.1145/2229163.2229175","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229175","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00452694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048144277","display_name":"Fr\u00e9d\u00e9rique Bassino","orcid":"https://orcid.org/0000-0002-0127-9352"},"institutions":[{"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/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9rique Bassino","raw_affiliation_strings":["Universit\u00e9 de Paris 13, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Paris 13, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047748726","display_name":"Julien Cl\u00e9ment","orcid":"https://orcid.org/0000-0001-8365-3899"},"institutions":[{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julien Cl\u00e9ment","raw_affiliation_strings":["Universit\u00e9 de Caen, France","Universite de Caen, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Caen, France","institution_ids":["https://openalex.org/I98702875"]},{"raw_affiliation_string":"Universite de Caen, France","institution_ids":["https://openalex.org/I98702875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071993530","display_name":"Pierre Nicod\u00e8me","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Nicod\u00e8me","raw_affiliation_strings":["\u00c9cole Polytechnique, France","Ecole polytechnique, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique, France","institution_ids":["https://openalex.org/I142476485"]},{"raw_affiliation_string":"Ecole polytechnique, France#TAB#","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.922,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.8224612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"3","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9995999932289124,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9995999932289124,"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":0.9994000196456909,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.7441596984863281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7035049200057983},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6810342073440552},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6139662265777588},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.6057252287864685},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5796983242034912},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4784660041332245},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.45648548007011414},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.44806185364723206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44474682211875916},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3955422639846802},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23839640617370605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20875772833824158}],"concepts":[{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.7441596984863281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7035049200057983},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6810342073440552},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6139662265777588},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.6057252287864685},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5796983242034912},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4784660041332245},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.45648548007011414},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.44806185364723206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44474682211875916},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3955422639846802},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23839640617370605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20875772833824158},{"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/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":2,"locations":[{"id":"doi:10.1145/2229163.2229175","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229175","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00452694v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00452694","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Algorithms, 2012, 8, pp.31:1--31:28. &#x27E8;10.1145/2229163.2229175&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00452694v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00452694","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Algorithms, 2012, 8, pp.31:1--31:28. &#x27E8;10.1145/2229163.2229175&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G11870515","display_name":"BOOLE: Quantifying Boolean Frameworks","funder_award_id":"ANR-09-BLAN-0011","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2084103371","display_name":null,"funder_award_id":"ANR-BLAN-2009-0011","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4200441373","display_name":null,"funder_award_id":"ANR-BLAN-2010-0204","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G849584761","display_name":"Algorithmic Methods for Non Uniform Random Generation, Models and Applications.","funder_award_id":"ANR-10-BLAN-0204","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W3242420","https://openalex.org/W64804145","https://openalex.org/W82544137","https://openalex.org/W158526756","https://openalex.org/W186403072","https://openalex.org/W191775444","https://openalex.org/W204059611","https://openalex.org/W341221793","https://openalex.org/W642038236","https://openalex.org/W654059483","https://openalex.org/W1491961545","https://openalex.org/W1496038746","https://openalex.org/W1504417041","https://openalex.org/W1541094831","https://openalex.org/W1597723816","https://openalex.org/W1603682988","https://openalex.org/W1871129629","https://openalex.org/W1890888469","https://openalex.org/W1949998359","https://openalex.org/W1971749553","https://openalex.org/W1981959436","https://openalex.org/W2005315460","https://openalex.org/W2015569722","https://openalex.org/W2016298115","https://openalex.org/W2019198417","https://openalex.org/W2026252457","https://openalex.org/W2034145759","https://openalex.org/W2045445781","https://openalex.org/W2053392780","https://openalex.org/W2056111563","https://openalex.org/W2058306852","https://openalex.org/W2061302137","https://openalex.org/W2063004022","https://openalex.org/W2068043943","https://openalex.org/W2075305839","https://openalex.org/W2078010999","https://openalex.org/W2094482767","https://openalex.org/W2099964107","https://openalex.org/W2109973210","https://openalex.org/W2340541605","https://openalex.org/W2581596983","https://openalex.org/W2911361414","https://openalex.org/W2912570624","https://openalex.org/W3016218058","https://openalex.org/W4254652536","https://openalex.org/W4318246088","https://openalex.org/W6603324235"],"related_works":["https://openalex.org/W2788344745","https://openalex.org/W2062336688","https://openalex.org/W2326614066","https://openalex.org/W2926906994","https://openalex.org/W2141075946","https://openalex.org/W2125199001","https://openalex.org/W1497842594","https://openalex.org/W2169695686","https://openalex.org/W2788566177","https://openalex.org/W3176806884"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"provide":[4,105],"the":[5,17,30,47,56,72,89,97,110,113],"multivariate":[6],"generating":[7,98],"function":[8,99],"counting":[9,35],"texts":[10],"according":[11],"to":[12,16,33,37,45],"their":[13],"length":[14],"and":[15,39,80,122],"number":[18,125],"of":[19,21,29,58,69,96,112,126,133,141],"occurrences":[20,127],"words":[22,59,66,135],"from":[23],"a":[24,85,101,106],"finite":[25,73,134],"set.":[26],"The":[27],"application":[28,140],"inclusion-exclusion":[31,114],"principle":[32],"word":[34],"due":[36],"Goulden":[38],"Jackson":[40],"[1979,":[41],"1983]":[42],"is":[43,60],"used":[44],"derive":[46],"result.":[48],"Unlike":[49],"some":[50],"other":[51],"techniques":[52],"which":[53],"suppose":[54],"that":[55],"set":[57,74],"reduced":[61],"(i.e.,":[62],"where":[63],"no":[64],"two":[65,130],"are":[67,136],"factor":[68],"one":[70],"another),":[71],"can":[75],"be":[76],"chosen":[77],"arbitrarily.":[78],"Noonan":[79],"Zeilberger":[81],"[1999]":[82],"already":[83],"provided":[84],"Maple":[86],"package":[87],"treating":[88],"nonreduced":[90],"case,":[91],"without":[92],"giving":[93],"an":[94,139],"expression":[95],"or":[100],"detailed":[102],"proof.":[103],"We":[104],"complete":[107],"proof":[108],"validating":[109],"use":[111],"principle.":[115],"Some":[116],"formul\u00e6":[117],"for":[118,124],"expected":[119],"values,":[120],"variance,":[121],"covariance":[123],"when":[128],"considering":[129],"arbitrary":[131],"sets":[132],"given":[137],"as":[138],"our":[142],"methodology.":[143]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2016-06-24T00:00:00"}
