{"id":"https://openalex.org/W2122990968","doi":"https://doi.org/10.1017/s0963548307008425","title":"The Distribution of Patterns in Random Trees","display_name":"The Distribution of Patterns in Random Trees","publication_year":2007,"publication_date":"2007-09-28","ids":{"openalex":"https://openalex.org/W2122990968","doi":"https://doi.org/10.1017/s0963548307008425","mag":"2122990968"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548307008425","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008425","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00001281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065051601","display_name":"Fr\u00e9d\u00e9ric Chyzak","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"FR\u00c9D\u00c9RIC CHYZAK","raw_affiliation_strings":["INRIA-Rocquencourt, F-78153 Le Chesnay cedex, France (e-mail:","Inria-rocquencourt, f-78153 le chesnay cedex, france (e-mail: frederic.chyzak@inria.fr)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA-Rocquencourt, F-78153 Le Chesnay cedex, France (e-mail:","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Inria-rocquencourt, f-78153 le chesnay cedex, france (e-mail: frederic.chyzak@inria.fr)#TAB#","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107303472","display_name":"Michael Drmota","orcid":"https://orcid.org/0000-0002-6876-6569"},"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":"MICHAEL DRMOTA","raw_affiliation_strings":["Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/113, A-1040 Wien, Austria (e-mail:","Institut f\u00fcr diskrete mathematik und geometrie, technische universit\u00e4t wien, wiedner hauptstra\u00dfe 8-10/113, a-1040 wien, austria (e-mail: michael.drmota@tuwien.ac.at, klausner@dmg.tu ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/113, A-1040 Wien, Austria (e-mail:","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr diskrete mathematik und geometrie, technische universit\u00e4t wien, wiedner hauptstra\u00dfe 8-10/113, a-1040 wien, austria (e-mail: michael.drmota@tuwien.ac.at, klausner@dmg.tu ...#TAB#","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045334960","display_name":"Thomas Klausner","orcid":null},"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":"THOMAS KLAUSNER","raw_affiliation_strings":["Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/113, A-1040 Wien, Austria (e-mail:","Institut f\u00fcr diskrete mathematik und geometrie, technische universit\u00e4t wien, wiedner hauptstra\u00dfe 8-10/113, a-1040 wien, austria (e-mail: michael.drmota@tuwien.ac.at, klausner@dmg.tu ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Diskrete Mathematik und Geometrie, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/113, A-1040 Wien, Austria (e-mail:","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr diskrete mathematik und geometrie, technische universit\u00e4t wien, wiedner hauptstra\u00dfe 8-10/113, a-1040 wien, austria (e-mail: michael.drmota@tuwien.ac.at, klausner@dmg.tu ...#TAB#","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060460393","display_name":"Gerard Kok","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"GERARD KOK","raw_affiliation_strings":["Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, NL-2628 CD Delft, The Netherlands (e-mail:","Delft institute of applied mathematics, delft university of technology, mekelweg 4, nl-2628 cd delft, the netherlands (e-mail: [email\u00a0protected])#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, NL-2628 CD Delft, The Netherlands (e-mail:","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft institute of applied mathematics, delft university of technology, mekelweg 4, nl-2628 cd delft, the netherlands (e-mail: [email\u00a0protected])#TAB#","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6641,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93321739,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"1","first_page":"21","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9986000061035156,"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":0.9986000061035156,"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/T11106","display_name":"Data Management and Algorithms","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9961000084877014,"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/mathematics","display_name":"Mathematics","score":0.8193783760070801},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.7373367547988892},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6475287675857544},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6391329169273376},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.6151372790336609},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5843846797943115},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5434338450431824},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4987044334411621},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4157288372516632},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3651690185070038},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23355919122695923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.053067803382873535}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8193783760070801},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.7373367547988892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6475287675857544},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6391329169273376},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6151372790336609},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5843846797943115},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5434338450431824},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4987044334411621},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4157288372516632},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3651690185070038},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23355919122695923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.053067803382873535},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548307008425","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008425","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.341.7129","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.341.7129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0605019v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.559.6094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.559.6094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/06/76/16/PDF/treepatterns.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.5929","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.5929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dmg.tuwien.ac.at/drmota/treepatterns2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00001281v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00001281","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":"2006","raw_type":"info:eu-repo/semantics/other"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00001281v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00001281","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":"2006","raw_type":"info:eu-repo/semantics/other"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W82068714","https://openalex.org/W1491178396","https://openalex.org/W1537139364","https://openalex.org/W1773520108","https://openalex.org/W1977847922","https://openalex.org/W1983188796","https://openalex.org/W1983809492","https://openalex.org/W1999132040","https://openalex.org/W2000062418","https://openalex.org/W2018547553","https://openalex.org/W2026252457","https://openalex.org/W2030794273","https://openalex.org/W2065095710","https://openalex.org/W2081508431","https://openalex.org/W2319000796","https://openalex.org/W2340541605","https://openalex.org/W2561675875","https://openalex.org/W4248663314","https://openalex.org/W4313336826"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3123626006","https://openalex.org/W3123025204","https://openalex.org/W1988122674","https://openalex.org/W2320787570","https://openalex.org/W2600496572","https://openalex.org/W2014320467","https://openalex.org/W1987144829","https://openalex.org/W4253988311","https://openalex.org/W2101483694"],"abstract_inverted_index":{"Let":[0],"$\\Tn{}$":[1,26],"denote":[2],"the":[3,34,43,68],"set":[4],"of":[5,9,25,42,45,47],"unrooted":[6],"labelled":[7],"trees":[8],"size":[10],"n":[11,38,64],"and":[12,55,61,71],"let":[13],"\u2133":[14,48],"be":[15],"a":[16],"particular":[17],"(finite,":[18],"unlabelled)":[19],"tree.":[20],"Assuming":[21],"that":[22,33],"every":[23],"tree":[24],"is":[27,31,49],"equally":[28],"likely,":[29],"it":[30],"shown":[32],"limiting":[35],"distribution":[36],"as":[37],"goes":[39],"to":[40,59],"infinity":[41],"number":[44],"occurrences":[46],"asymptotically":[50,57],"normal":[51],"with":[52],"mean":[53],"value":[54],"variance":[56],"equivalent":[58],"\u03bcn":[60],"\u03c3":[62],"2":[63],",":[65],"respectively,":[66],"where":[67],"constants":[69],"\u03bc>0":[70],"\u03c3\u22650":[72],"are":[73],"computable.":[74]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}