{"id":"https://openalex.org/W2056205129","doi":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","title":"On the joint distribution of the nodes in uniform multidimensional binary trees","display_name":"On the joint distribution of the nodes in uniform multidimensional binary trees","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W2056205129","doi":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","mag":"2056205129"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","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 and Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006800197","display_name":"Rainer Kemp","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Rainer Kemp","raw_affiliation_strings":["Johann Wolfgang Goethe-Universita\u0308t, Fachbereich Informatik, D-60054 Frankfurt am Main, Germany","Johann Wolfgang Goethe\u2010Universit\u00e4t, Fachbereich Informatik, D\u201060054 Frankfurt am Main, Germany"],"affiliations":[{"raw_affiliation_string":"Johann Wolfgang Goethe-Universita\u0308t, Fachbereich Informatik, D-60054 Frankfurt am Main, Germany","institution_ids":["https://openalex.org/I114090438"]},{"raw_affiliation_string":"Johann Wolfgang Goethe\u2010Universit\u00e4t, Fachbereich Informatik, D\u201060054 Frankfurt am Main, Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006800197"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.21017403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"3-4","first_page":"261","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.95660001039505,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9253000020980835,"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/binary-number","display_name":"Binary number","score":0.6419200897216797},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.6326277256011963},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6177245378494263},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5898706912994385},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5838640928268433},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.5665059685707092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5641113519668579},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.5537784099578857},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5345349311828613},{"id":"https://openalex.org/keywords/joint","display_name":"Joint (building)","score":0.4773012399673462},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4486871659755707},{"id":"https://openalex.org/keywords/struct","display_name":"struct","score":0.44138070940971375},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"Uniform distribution (continuous)","score":0.41973716020584106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3667662739753723},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36649852991104126},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17574891448020935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11087137460708618},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.06872859597206116}],"concepts":[{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6419200897216797},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.6326277256011963},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6177245378494263},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5898706912994385},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5838640928268433},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.5665059685707092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5641113519668579},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.5537784099578857},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5345349311828613},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.4773012399673462},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4486871659755707},{"id":"https://openalex.org/C2776142590","wikidata":"https://www.wikidata.org/wiki/Q1164699","display_name":"struct","level":2,"score":0.44138070940971375},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.41973716020584106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3667662739753723},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36649852991104126},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17574891448020935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11087137460708618},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.06872859597206116},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C170154142","wikidata":"https://www.wikidata.org/wiki/Q150737","display_name":"Architectural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<261::aid-rsa5>3.0.co;2-t","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 and Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1548210529","https://openalex.org/W2951678044","https://openalex.org/W1510719821","https://openalex.org/W2123024824","https://openalex.org/W4300450359","https://openalex.org/W3022865202","https://openalex.org/W2117536196","https://openalex.org/W2382364329","https://openalex.org/W2501849745","https://openalex.org/W2019778981"],"abstract_inverted_index":{"Multidimensional":[0],"binary":[1,30],"trees":[2,7,19],"represent":[3],"a":[4,28,63,77],"symbiosis":[5],"of":[6,17,25,51,54,73],"and":[8,10,59,66],"tries,":[9],"they":[11],"essentially":[12],"arise":[13],"in":[14,27,42,62,81],"the":[15,39,43,48,52,70],"construction":[16],"search":[18],"for":[20],"multidimensional":[21],"keys.":[22],"The":[23],"set":[24],"nodes":[26,40,55,74],"d-dimensional":[29],"tree":[31],"can":[32],"be":[33],"partitioned":[34],"into":[35],"layers":[36],"according":[37],"to":[38],"appearing":[41],"ith":[44],"dimension.":[45],"We":[46],"determine":[47],"exact":[49],"distribution":[50,80,87],"number":[53],"with":[56],"zero,":[57],"one,":[58],"two":[60],"sons":[61],"specified":[64],"layer":[65],"show":[67],"that":[68],"jointly":[69],"three":[71],"types":[72],"asymptotically":[75],"have":[76],"trivariate":[78,85],"normal":[79,86],"each":[82],"layer.":[83],"That":[84],"is":[88],"completely":[89],"characterized.":[90],"\u00a9":[91],"1998":[92,103],"John":[93],"Wiley":[94],"&":[95],"Sons,":[96],"Inc.":[97],"Random":[98],"Struct.":[99],"Alg.,":[100],"13:":[101],"261\u2013283,":[102]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
