{"id":"https://openalex.org/W4401201741","doi":"https://doi.org/10.48550/arxiv.2407.19454","title":"The $B_2$ index of galled trees","display_name":"The $B_2$ index of galled trees","publication_year":2024,"publication_date":"2024-07-28","ids":{"openalex":"https://openalex.org/W4401201741","doi":"https://doi.org/10.48550/arxiv.2407.19454"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-04717043v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04717043","pdf_url":"http://arxiv.org/pdf/2407.19454","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"info:eu-repo/semantics/preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2407.19454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089526706","display_name":"Fran\u00e7ois Bienvenu","orcid":"https://orcid.org/0000-0002-5396-1193","observed_orcids":["https://orcid.org/0000-0002-5396-1193"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4387152972","display_name":"Laboratoire de Math\u00e9matiques de Besan\u00e7on","ror":"https://ror.org/04nrhwg12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387152972","https://openalex.org/I4405256580"]},{"id":"https://openalex.org/I4405257222","display_name":"ETH Institute for Theoretical Studies","ror":"https://ror.org/051d04622","country_code":"CH","type":"facility","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4405257222"]},{"id":"https://openalex.org/I90843659","display_name":"Universit\u00e9 de Franche-Comt\u00e9","ror":"https://ror.org/03pcc9z86","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405256580","https://openalex.org/I90843659"]}],"countries":["CH","FR"],"is_corresponding":false,"raw_author_name":"Bienvenu, Fran\u00e7ois","raw_affiliation_strings":["Institute for Theoretical Studies , ETH Z\u00fcrich , 8092 Z\u00fcrich , Switzerland","Universit\u00e9 de Franche-Comt\u00e9 , CNRS , LmB , F-25000 Besan\u00e7on , France","Institute for Theoretical Studies [Z\u00fcrich] (ETH Z\u00fcrich, , 8092 Z\u00fcrich, Switzerland - Switzerland)","LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Studies , ETH Z\u00fcrich , 8092 Z\u00fcrich , Switzerland","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4405257222"]},{"raw_affiliation_string":"Universit\u00e9 de Franche-Comt\u00e9 , CNRS , LmB , F-25000 Besan\u00e7on , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I90843659"]},{"raw_affiliation_string":"Institute for Theoretical Studies [Z\u00fcrich] (ETH Z\u00fcrich, , 8092 Z\u00fcrich, Switzerland - Switzerland)","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4405257222"]},{"raw_affiliation_string":"LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)","institution_ids":["https://openalex.org/I4387152972","https://openalex.org/I90843659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066398937","display_name":"Jean\u2010Jil Duchamps","orcid":"https://orcid.org/0000-0002-3823-1686","observed_orcids":["https://orcid.org/0000-0002-3823-1686"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4387152972","display_name":"Laboratoire de Math\u00e9matiques de Besan\u00e7on","ror":"https://ror.org/04nrhwg12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387152972","https://openalex.org/I4405256580"]},{"id":"https://openalex.org/I90843659","display_name":"Universit\u00e9 de Franche-Comt\u00e9","ror":"https://ror.org/03pcc9z86","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405256580","https://openalex.org/I90843659"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Duchamps, Jean-Jil","raw_affiliation_strings":["Universit\u00e9 de Franche-Comt\u00e9 , CNRS , LmB , F-25000 Besan\u00e7on , France","LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Franche-Comt\u00e9 , CNRS , LmB , F-25000 Besan\u00e7on , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I90843659"]},{"raw_affiliation_string":"LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)","institution_ids":["https://openalex.org/I4387152972","https://openalex.org/I90843659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000390095","display_name":"Michael Fuchs","orcid":"https://orcid.org/0000-0001-8891-6897","observed_orcids":["https://orcid.org/0000-0001-8891-6897"]},"institutions":[{"id":"https://openalex.org/I87354575","display_name":"National Chengchi University","ror":"https://ror.org/03rqk8h36","country_code":"TW","type":"education","lineage":["https://openalex.org/I87354575"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Fuchs, Michael","raw_affiliation_strings":["Department of Mathematical Sciences , National Chengchi University , Taipei 116 , Taiwan","NCCU - National ChengChi University [Taipei] (NO.64,Sec.2,ZhiNan Rd.,Wenshan District,Taipei City 11605,Taiwan (R.O.C) - Taiwan)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , National Chengchi University , Taipei 116 , Taiwan","institution_ids":["https://openalex.org/I87354575"]},{"raw_affiliation_string":"NCCU - National ChengChi University [Taipei] (NO.64,Sec.2,ZhiNan Rd.,Wenshan District,Taipei City 11605,Taiwan (R.O.C) - Taiwan)","institution_ids":["https://openalex.org/I87354575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028644665","display_name":"Tsan\u2010Cheng Yu","orcid":"https://orcid.org/0009-0000-3653-255X","observed_orcids":["https://orcid.org/0009-0000-3653-255X"]},"institutions":[{"id":"https://openalex.org/I87354575","display_name":"National Chengchi University","ror":"https://ror.org/03rqk8h36","country_code":"TW","type":"education","lineage":["https://openalex.org/I87354575"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu, Tsan-Cheng","raw_affiliation_strings":["Department of Mathematical Sciences , National Chengchi University , Taipei 116 , Taiwan","NCCU - National ChengChi University [Taipei] (NO.64,Sec.2,ZhiNan Rd.,Wenshan District,Taipei City 11605,Taiwan (R.O.C) - Taiwan)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , National Chengchi University , Taipei 116 , Taiwan","institution_ids":["https://openalex.org/I87354575"]},{"raw_affiliation_string":"NCCU - National ChengChi University [Taipei] (NO.64,Sec.2,ZhiNan Rd.,Wenshan District,Taipei City 11605,Taiwan (R.O.C) - Taiwan)","institution_ids":["https://openalex.org/I87354575"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.3889000117778778,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.3889000117778778,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.30959999561309814,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.042399998754262924,"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/phylogenetic-networks","display_name":"phylogenetic networks","score":0.972000002861023},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.7580000162124634},{"id":"https://openalex.org/keywords/moments","display_name":"moments","score":0.5220000147819519},{"id":"https://openalex.org/keywords/local-limit","display_name":"local limit","score":0.8270000219345093},{"id":"https://openalex.org/keywords/analytic-combinatorics","display_name":"analytic combinatorics","score":0.9890000224113464}],"concepts":[{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.7043541669845581},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6454927325248718},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6260350942611694},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.6012167930603027},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5761985182762146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5624997019767761},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.49792981147766113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47623756527900696},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45586490631103516},{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.44435518980026245},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4414397180080414},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3403359651565552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3390653133392334},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.1635122001171112},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16004040837287903},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1148400604724884},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-04717043v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04717043","pdf_url":"http://arxiv.org/pdf/2407.19454","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:arXiv.org:2407.19454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2407.19454","pdf_url":"https://arxiv.org/pdf/2407.19454","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2407.19454","doi":"https://doi.org/10.48550/arxiv.2407.19454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2407.19454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04717043v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04717043","pdf_url":"http://arxiv.org/pdf/2407.19454","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G529282299","display_name":"Random Graphs and Phylogenetic Networks","funder_award_id":"ANR-24-CE40-7154","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"},{"id":"https://openalex.org/F4320327714","display_name":"ETH Z\u00fcrich Foundation","ror":"https://ror.org/03nqkz164"},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401201741.pdf","grobid_xml":"https://content.openalex.org/works/W4401201741.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1678521545","https://openalex.org/W1976084081","https://openalex.org/W2006252824","https://openalex.org/W2017170340","https://openalex.org/W2021288877","https://openalex.org/W2090793976","https://openalex.org/W2097361203","https://openalex.org/W2120547819","https://openalex.org/W2547104173","https://openalex.org/W2802739963","https://openalex.org/W2974444353","https://openalex.org/W3198283169","https://openalex.org/W3215141734","https://openalex.org/W4225693218","https://openalex.org/W4232661759","https://openalex.org/W4234972612","https://openalex.org/W4235071074","https://openalex.org/W4298295580","https://openalex.org/W4308420880","https://openalex.org/W4392733169","https://openalex.org/W4399811152","https://openalex.org/W4401411014","https://openalex.org/W4408845852"],"related_works":["https://openalex.org/W7202072138","https://openalex.org/W3092914070","https://openalex.org/W7165769241","https://openalex.org/W3198283169","https://openalex.org/W4408845852","https://openalex.org/W4388088139","https://openalex.org/W2923291801","https://openalex.org/W2793301855","https://openalex.org/W3094573588","https://openalex.org/W2094647384"],"abstract_inverted_index":{"In":[0,40],"recent":[1],"years,":[2],"there":[3],"has":[4,100,158],"been":[5,101,161],"an":[6,173],"effort":[7],"to":[8,23,31,87,103,163,188],"extend":[9],"the":[10,19,27,36,45,60,73,79,93,167],"classical":[11],"notion":[12],"of":[13,21,26,52,63,106,115],"phylogenetic":[14,53,111],"balance,":[15],"originally":[16],"defined":[17],"in":[18,70,182],"context":[20],"trees,":[22],"networks.":[24],"One":[25,113],"most":[28],"natural":[29],"ways":[30],"do":[32],"this":[33,41,104,116,178],"is":[34,92,118,140,180],"with":[35,128],"so-called":[37],"$B_2$":[38,46,61],"index.":[39],"paper,":[42],"we":[43,120],"study":[44,164],"index":[47,62,99],"for":[48,108],"a":[49,64,85,97,109],"prominent":[50],"class":[51],"networks:":[54],"galled":[55,67],"trees.":[56],"We":[57,77],"show":[58],"that":[59,96,119],"uniform":[65],"leaf-labeled":[66],"tree":[68],"converges":[69],"distribution":[71],"as":[72,143],"network":[74],"becomes":[75],"large.":[76],"characterize":[78],"corresponding":[80],"limiting":[81],"distribution,":[82],"and":[83,124,133,184],"provide":[84],"way":[86],"compute":[88],"its":[89,129],"moments.":[90],"This":[91],"first":[94],"time":[95],"balance":[98],"studied":[102],"level":[105],"detail":[107],"random":[110],"network.":[112],"specificity":[114],"work":[117],"use":[121],"two":[122],"different":[123],"independent":[125],"approaches,":[126],"each":[127],"advantages:":[130],"analytic":[131,137],"combinatorics,":[132],"local":[134,168],"limits.":[135],"The":[136],"combinatorics":[138],"approach":[139,170],"more":[141,153],"direct,":[142],"it":[144,150,157],"relies":[145],"on":[146],"standard":[147],"tools;":[148],"but":[149],"involves":[151],"slightly":[152],"complex":[154],"calculations.":[155],"Because":[156],"not":[159],"previously":[160],"used":[162,187],"such":[165],"questions,":[166],"limit":[169],"requires":[171],"developing":[172],"extensive":[174],"framework":[175,179],"beforehand;":[176],"however,":[177],"interesting":[181],"itself":[183],"can":[185],"be":[186],"tackle":[189],"other":[190],"similar":[191],"problems.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-08-01T00:00:00"}
