{"id":"https://openalex.org/W2753856963","doi":"https://doi.org/10.1017/s0963548318000512","title":"Inversions in Split Trees and Conditional Galton\u2013Watson Trees","display_name":"Inversions in Split Trees and Conditional Galton\u2013Watson Trees","publication_year":2018,"publication_date":"2018-10-31","ids":{"openalex":"https://openalex.org/W2753856963","doi":"https://doi.org/10.1017/s0963548318000512","mag":"2753856963"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548318000512","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000512","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.00216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008760479","display_name":"Xing Shi Cai","orcid":"https://orcid.org/0000-0002-3768-8078"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"XING SHI CAI","raw_affiliation_strings":["Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018224596","display_name":"Cecilia Holmgren","orcid":"https://orcid.org/0000-0003-0717-4671"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"CECILIA HOLMGREN","raw_affiliation_strings":["Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022615833","display_name":"Svante Janson","orcid":"https://orcid.org/0000-0002-9680-2790"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"SVANTE JANSON","raw_affiliation_strings":["Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070055736","display_name":"Tony Johansson","orcid":"https://orcid.org/0000-0002-9264-3462"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"TONY JOHANSSON","raw_affiliation_strings":["Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037558079","display_name":"Fiona Skerman","orcid":"https://orcid.org/0000-0003-4141-7059"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"FIONA SKERMAN","raw_affiliation_strings":["Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Uppsala University, L\u00e4gerhyddsv\u00e4gen 1, 752 37 Uppsala, Sweden (e-mail:","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5008760479"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":null,"apc_paid":null,"fwci":1.8445,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82661917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"3","first_page":"335","last_page":"364"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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":0.9998999834060669,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.998199999332428,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9962999820709229,"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/mathematics","display_name":"Mathematics","score":0.8315644264221191},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7718970775604248},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5737285614013672},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5433270931243896},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5346189141273499},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5017063617706299},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.47794583439826965},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4535835385322571},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4208352863788605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10923188924789429}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8315644264221191},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7718970775604248},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5737285614013672},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5433270931243896},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5346189141273499},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5017063617706299},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47794583439826965},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4535835385322571},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4208352863788605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10923188924789429},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0963548318000512","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548318000512","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:research-information.bris.ac.uk:openaire_cris_publications/5f7bf45e-f6da-454f-8ad6-ecd0263799f7","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/5f7bf45e-f6da-454f-8ad6-ecd0263799f7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Skerman, F, Cai, X S, Holmgren, C, Janson, S & Johansson, T 2019, 'Inversions in split trees and conditional Galton-Watson trees', Combinatorics, Probability and Computing, pp. 335-364. https://doi.org/10.1017/S0963548318000512","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1709.00216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.00216","pdf_url":"https://arxiv.org/pdf/1709.00216","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/5f7bf45e-f6da-454f-8ad6-ecd0263799f7","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/5f7bf45e-f6da-454f-8ad6-ecd0263799f7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.4230/lipics.aofa.2018.15","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.aofa.2018.15","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.00216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.00216","pdf_url":"https://arxiv.org/pdf/1709.00216","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8683756101","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse"}],"funders":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W58305343","https://openalex.org/W158955491","https://openalex.org/W1016654151","https://openalex.org/W1511251174","https://openalex.org/W1523300416","https://openalex.org/W1544198293","https://openalex.org/W1584623820","https://openalex.org/W1659198685","https://openalex.org/W1676383271","https://openalex.org/W1854279212","https://openalex.org/W1968621471","https://openalex.org/W1970128728","https://openalex.org/W1978795682","https://openalex.org/W1979228272","https://openalex.org/W1993618625","https://openalex.org/W1998626965","https://openalex.org/W2002963750","https://openalex.org/W2004025893","https://openalex.org/W2008196645","https://openalex.org/W2009826756","https://openalex.org/W2010999517","https://openalex.org/W2022718961","https://openalex.org/W2027482003","https://openalex.org/W2039359759","https://openalex.org/W2039379906","https://openalex.org/W2041147307","https://openalex.org/W2042464140","https://openalex.org/W2043264962","https://openalex.org/W2043392316","https://openalex.org/W2059932393","https://openalex.org/W2081564088","https://openalex.org/W2090682229","https://openalex.org/W2094482767","https://openalex.org/W2095181329","https://openalex.org/W2103012681","https://openalex.org/W2110042562","https://openalex.org/W2111726541","https://openalex.org/W2113913510","https://openalex.org/W2120547819","https://openalex.org/W2157071288","https://openalex.org/W2165547676","https://openalex.org/W2166677052","https://openalex.org/W2168916654","https://openalex.org/W2169071224","https://openalex.org/W2240076435","https://openalex.org/W2262370168","https://openalex.org/W2578965661","https://openalex.org/W2582679126","https://openalex.org/W2658208876","https://openalex.org/W2751862591","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W2797135730","https://openalex.org/W2809600437","https://openalex.org/W2962801705","https://openalex.org/W3102907094","https://openalex.org/W3104507472","https://openalex.org/W3104565967","https://openalex.org/W4231805375","https://openalex.org/W4232753567","https://openalex.org/W4233413206","https://openalex.org/W4235295823","https://openalex.org/W4240348261","https://openalex.org/W4247899490","https://openalex.org/W4254826564","https://openalex.org/W4255611719","https://openalex.org/W4292070112","https://openalex.org/W4301441647","https://openalex.org/W6637497450","https://openalex.org/W6660250807","https://openalex.org/W6676867134","https://openalex.org/W6820127409"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W184455116","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2390235546"],"abstract_inverted_index":{"We":[0,29],"study":[1],"I":[2,36,68],"(":[3,37,69],"T":[4,13,38,50,70,78,83,114,136],"),":[5,72],"the":[6,33,44,54,64,103,127,161,166],"number":[7],"of":[8,25,35,49,53,67,76,105,130,156],"inversions":[9,26,164],"in":[10,27,96,154],"a":[11,23,74,88,131,150],"tree":[12],"with":[14],"its":[15],"vertices":[16],"labelled":[17],"uniformly":[18],"at":[19],"random,":[20],"which":[21],"is":[22],"generalization":[24],"permutations.":[28],"first":[30],"show":[31,121,144],"that":[32,122,145,176],"cumulants":[34],")":[39],"have":[40],"explicit":[41],"formulas":[42],"involving":[43],"k":[45],"-total":[46],"common":[47],"ancestors":[48],"(an":[51],"extension":[52],"total":[55,167],"path":[56,168],"length).":[57],"Then":[58],"we":[59,86,101,120,143,170],"consider":[60],"X":[61,92,106,123,146],"n":[62,71,79,84,93,107,115,124,137,147],",":[63],"normalized":[65],"version":[66],"for":[73,91,108],"sequence":[75],"trees":[77,118],".":[80],"For":[81,113],"fixed":[82],"'s,":[85],"prove":[87],"sufficient":[89],"condition":[90],"to":[94,126,149,173],"converge":[95],"distribution.":[97],"As":[98],"an":[99],"application,":[100],"identify":[102],"limit":[104],"complete":[109],"b":[110],"-ary":[111],"trees.":[112],"being":[116],"split":[117],"[16],":[119],"converges":[125,148],"unique":[128],"solution":[129],"distributional":[132],"equation.":[133],"Finally,":[134],"when":[135],"'s":[138],"are":[139,171],"conditional":[140],"Galton\u2013Watson":[141],"trees,":[142],"random":[151],"variable":[152],"defined":[153],"terms":[155],"Brownian":[157],"excursions.":[158],"By":[159],"exploiting":[160],"connection":[162],"between":[163],"and":[165,179,185],"length,":[169],"able":[172],"give":[174],"results":[175],"significantly":[177],"strengthen":[178],"broaden":[180],"previous":[181],"work":[182],"by":[183],"Panholzer":[184],"Seitz":[186],"[46].":[187]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-11-23T00:00:00"}