{"id":"https://openalex.org/W2073792589","doi":"https://doi.org/10.1002/rsa.3240030309","title":"Generalized Digital Trees and Their Difference\u2014Differential Equations","display_name":"Generalized Digital Trees and Their Difference\u2014Differential Equations","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W2073792589","doi":"https://doi.org/10.1002/rsa.3240030309","mag":"2073792589"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240030309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240030309","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00075137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018743761","display_name":"Philippe Flajolet","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Philippe Flajolet","raw_affiliation_strings":["Algorithms Project, INRIA Rocquencourt, F-78153 Le Chesnay, France","Algorithms Project, INRIA\u2010Rocquencourt, F\u201078153 Le Chesnay, France"],"affiliations":[{"raw_affiliation_string":"Algorithms Project, INRIA Rocquencourt, F-78153 Le Chesnay, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Algorithms Project, INRIA\u2010Rocquencourt, F\u201078153 Le Chesnay, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051530602","display_name":"Bruce M. Richmond","orcid":"https://orcid.org/0000-0002-0056-5832"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bruce Richmond","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L, 3G1, Canada","Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario,  N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L, 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario,  N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018743761"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":10.0446,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.9805686,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"3","issue":"3","first_page":"305","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9994000196456909,"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":0.9994000196456909,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9966999888420105,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.6851760745048523},{"id":"https://openalex.org/keywords/trie","display_name":"Trie","score":0.6360754370689392},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.6102162003517151},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.551028311252594},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5355643630027771},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4691699147224426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4268651306629181},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4120649993419647},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41186630725860596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3237420320510864},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32166969776153564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2805274426937103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26593485474586487},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.16724750399589539}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6851760745048523},{"id":"https://openalex.org/C190290938","wikidata":"https://www.wikidata.org/wiki/Q387015","display_name":"Trie","level":3,"score":0.6360754370689392},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.6102162003517151},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.551028311252594},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5355643630027771},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4691699147224426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4268651306629181},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4120649993419647},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41186630725860596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3237420320510864},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32166969776153564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2805274426937103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26593485474586487},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.16724750399589539},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1002/rsa.3240030309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240030309","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"},{"id":"pmh:hdl:10068/57273","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/57273","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.9820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://algo.inria.fr/flajolet/Publications/FlRi92.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.9331","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.9331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.inria.fr/INRIA/Projects/algo/web/flajolet/Publications/b-digital.ps.gz","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00075137v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00075137","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":"[Research Report] RR-1423, INRIA. 1991","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00075137v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00075137","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":"[Research Report] RR-1423, INRIA. 1991","raw_type":"Reports"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W46381831","https://openalex.org/W579204254","https://openalex.org/W1491940285","https://openalex.org/W1569990823","https://openalex.org/W1585108299","https://openalex.org/W1597637931","https://openalex.org/W1971361861","https://openalex.org/W1972501887","https://openalex.org/W1974784305","https://openalex.org/W1978795682","https://openalex.org/W2008052995","https://openalex.org/W2008436978","https://openalex.org/W2018919817","https://openalex.org/W2020658344","https://openalex.org/W2052638374","https://openalex.org/W2066828720","https://openalex.org/W2072435040","https://openalex.org/W2072501876","https://openalex.org/W2078830190","https://openalex.org/W2080028582","https://openalex.org/W2087966340","https://openalex.org/W2125838758","https://openalex.org/W2132750992","https://openalex.org/W2575871956","https://openalex.org/W2658866131","https://openalex.org/W2752853835","https://openalex.org/W3189934495","https://openalex.org/W4235371190","https://openalex.org/W4250378179"],"related_works":["https://openalex.org/W104884668","https://openalex.org/W3112332783","https://openalex.org/W2120071517","https://openalex.org/W2406489341","https://openalex.org/W2344797854","https://openalex.org/W2113746559","https://openalex.org/W2080508516","https://openalex.org/W2006638646","https://openalex.org/W4286751119","https://openalex.org/W2043671984"],"abstract_inverted_index":{"Abstract":[0],"Consider":[1],"a":[2,18,22,33,68,106],"tree":[3,19,41,66],"partitioning":[4],"process":[5],"in":[6,118],"which":[7],"n":[8],"elements":[9],"are":[10],"split":[11],"into":[12,29],"b":[13,21,73],"at":[14],"the":[15,25,48,52,61,65],"root":[16],"of":[17,44,64,71,92,101,109,124],"(":[20],"design":[23],"parameter),":[24],"rest":[26],"going":[27,80],"recursively":[28],"two":[30],"subtrees":[31],"with":[32],"binomial":[34],"probability":[35],"distribution.":[36],"This":[37],"extends":[38],"some":[39,102],"familiar":[40],"data":[42],"structures":[43,114],"computer":[45],"science":[46],"like":[47],"digital":[49,53,113],"trie":[50],"and":[51,95],"search":[54],"tree.":[55],"The":[56,77,98],"exponential":[57],"generating":[58,86,126],"function":[59],"for":[60],"expected":[62],"size":[63],"satisfies":[67],"difference\u2013differential":[69],"equation":[70],"order":[72],",":[74],"magnified":[75],"image":[76],"solution":[78],"involves":[79],"to":[81],"ordinary":[82,125],"(rather":[83],"than":[84],"exponential)":[85],"functions,":[87],"analyzing":[88],"singularities":[89],"by":[90],"means":[91],"Mellin":[93],"transforms":[94],"contour":[96],"integration.":[97],"method":[99],"is":[100],"general":[103],"interest":[104],"since":[105],"large":[107],"number":[108],"related":[110],"problems":[111],"on":[112],"can":[115],"be":[116],"treated":[117],"this":[119],"way":[120],"via":[121],"singularity":[122],"analysis":[123],"functions.":[127]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
