{"id":"https://openalex.org/W1504761530","doi":"https://doi.org/10.37236/1089","title":"Counting Rooted Trees: The Universal Law $t(n)\\,\\sim\\,C \\rho^{-n} n^{-3/2}$","display_name":"Counting Rooted Trees: The Universal Law $t(n)\\,\\sim\\,C \\rho^{-n} n^{-3/2}$","publication_year":2006,"publication_date":"2006-08-03","ids":{"openalex":"https://openalex.org/W1504761530","doi":"https://doi.org/10.37236/1089","mag":"1504761530"},"language":"en","primary_location":{"id":"doi:10.37236/1089","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1089","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r63/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r63/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056883446","display_name":"Jason P. Bell","orcid":"https://orcid.org/0000-0002-2873-4482"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"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"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Jason P. Bell","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060761505","display_name":"Stanley Burris","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"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"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Stanley N. Burris","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040147498","display_name":"Karen Yeats","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"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"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Karen A. Yeats","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada","Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC,V5A 1S6 Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Boston University 111 Cummington Street, Boston, MA 02215 USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8393,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.89010526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9977999925613403,"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":0.9955000281333923,"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":0.8892906904220581},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.8862662315368652},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8122521638870239},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"Radius of convergence","score":0.7099646329879761},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5905308723449707},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5368607044219971},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5239613056182861},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45569485425949097},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4346114993095398},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4252641797065735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3759959638118744},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07868605852127075},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.06462234258651733}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8892906904220581},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.8862662315368652},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8122521638870239},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.7099646329879761},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5905308723449707},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5368607044219971},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5239613056182861},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45569485425949097},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4346114993095398},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4252641797065735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3759959638118744},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07868605852127075},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.06462234258651733},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":1,"locations":[{"id":"doi:10.37236/1089","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1089","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r63/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1089","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1089","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r63/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1504761530.pdf","grobid_xml":"https://content.openalex.org/works/W1504761530.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W82672431","https://openalex.org/W766989500","https://openalex.org/W935842532","https://openalex.org/W1489095222","https://openalex.org/W1574394872","https://openalex.org/W1582129286","https://openalex.org/W1981733036","https://openalex.org/W1983188796","https://openalex.org/W2001332273","https://openalex.org/W2007225893","https://openalex.org/W2009210880","https://openalex.org/W2018919817","https://openalex.org/W2028771687","https://openalex.org/W2032180500","https://openalex.org/W2035160364","https://openalex.org/W2045390532","https://openalex.org/W2069766942","https://openalex.org/W2101041418","https://openalex.org/W2151068277","https://openalex.org/W2319000796","https://openalex.org/W2340541605","https://openalex.org/W2481201629","https://openalex.org/W2484547531","https://openalex.org/W2795721869","https://openalex.org/W3140559000","https://openalex.org/W4205898702","https://openalex.org/W4243107850","https://openalex.org/W4300488561"],"related_works":["https://openalex.org/W4300455649","https://openalex.org/W2296588302","https://openalex.org/W4328119206","https://openalex.org/W2033245919","https://openalex.org/W4252409532","https://openalex.org/W2006067547","https://openalex.org/W9228044","https://openalex.org/W2951215358","https://openalex.org/W1504761530","https://openalex.org/W2527460344"],"abstract_inverted_index":{"Combinatorial":[0],"classes":[1],"${\\cal":[2],"T}$":[3],"that":[4,47,57],"are":[5],"recursively":[6],"defined":[7],"using":[8],"combinations":[9],"of":[10,32,36,50,61,72,74],"the":[11,48,51,54,59,70],"standard":[12],"multiset,":[13],"sequence,":[14],"directed":[15],"cycle":[16,18],"and":[17,20],"constructions,":[19],"their":[21],"restrictions,":[22],"have":[23],"generating":[24],"series":[25],"${\\bf":[26,75],"T}(z)$":[27],"with":[28],"a":[29,38],"positive":[30],"radius":[31,71],"convergence;":[33],"for":[34,58],"most":[35],"these":[37],"simple":[39],"test":[40],"can":[41],"be":[42],"used":[43],"to":[44],"quickly":[45],"show":[46],"form":[49],"asymptotics":[52],"is":[53,69],"same":[55],"as":[56],"class":[60],"rooted":[62],"trees:":[63],"$C":[64],"\\rho^{-n}":[65],"n^{-3/2}$,":[66],"where":[67],"$\\rho$":[68],"convergence":[73],"T}$.":[76]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
