{"id":"https://openalex.org/W3147028298","doi":"https://doi.org/10.5070/c63362791","title":"The combinatorics of a tree-like functional equation for connected chord diagrams","display_name":"The combinatorics of a tree-like functional equation for connected chord diagrams","publication_year":2023,"publication_date":"2023-12-22","ids":{"openalex":"https://openalex.org/W3147028298","doi":"https://doi.org/10.5070/c63362791","mag":"3147028298"},"language":"en","primary_location":{"id":"doi:10.5070/c63362791","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362791","pdf_url":"https://escholarship.org/content/qt1qg5647z/qt1qg5647z.pdf?t=s622w9","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt1qg5647z/qt1qg5647z.pdf?t=s622w9","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023317979","display_name":"Lukas Nabergall","orcid":null},"institutions":[{"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"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Lukas Nabergall","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023317979"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.668,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51117784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"3","issue":"3","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":0.9988999962806702,"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":0.9988999962806702,"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/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9625999927520752,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/bijection","display_name":"Bijection","score":0.7777508497238159},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.6951444745063782},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.649070680141449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6428742408752441},{"id":"https://openalex.org/keywords/chord","display_name":"Chord (peer-to-peer)","score":0.4623791575431824},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43481260538101196},{"id":"https://openalex.org/keywords/enumerative-combinatorics","display_name":"Enumerative combinatorics","score":0.42636430263519287},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4195188283920288},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40020623803138733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21471473574638367}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7777508497238159},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.6951444745063782},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.649070680141449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6428742408752441},{"id":"https://openalex.org/C194147245","wikidata":"https://www.wikidata.org/wiki/Q1076368","display_name":"Chord (peer-to-peer)","level":2,"score":0.4623791575431824},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43481260538101196},{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.42636430263519287},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4195188283920288},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40020623803138733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21471473574638367},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5070/c63362791","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362791","pdf_url":"https://escholarship.org/content/qt1qg5647z/qt1qg5647z.pdf?t=s622w9","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.02296","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.02296","pdf_url":"https://arxiv.org/pdf/2104.02296","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":"","raw_type":"text"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt1qg5647z","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/1qg5647z","pdf_url":"https://escholarship.org/content/qt1qg5647z/qt1qg5647z.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorial Theory, vol 3, iss 3","raw_type":"article"},{"id":"doi:10.48550/arxiv.2104.02296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.02296","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.5070/c63362791","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63362791","pdf_url":"https://escholarship.org/content/qt1qg5647z/qt1qg5647z.pdf?t=s622w9","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3147028298.pdf","grobid_xml":"https://content.openalex.org/works/W3147028298.grobid-xml"},"referenced_works_count":77,"referenced_works":["https://openalex.org/W1955029","https://openalex.org/W166539567","https://openalex.org/W186403072","https://openalex.org/W219446931","https://openalex.org/W1521045270","https://openalex.org/W1526338362","https://openalex.org/W1528326162","https://openalex.org/W1530744624","https://openalex.org/W1563213005","https://openalex.org/W1625071253","https://openalex.org/W1667848118","https://openalex.org/W1964355300","https://openalex.org/W1971351183","https://openalex.org/W1971843463","https://openalex.org/W1972912363","https://openalex.org/W1973641495","https://openalex.org/W1978490496","https://openalex.org/W1987867438","https://openalex.org/W1992104349","https://openalex.org/W1995036450","https://openalex.org/W1996008071","https://openalex.org/W2018335206","https://openalex.org/W2021913191","https://openalex.org/W2023353776","https://openalex.org/W2025178706","https://openalex.org/W2025746238","https://openalex.org/W2038711832","https://openalex.org/W2042682183","https://openalex.org/W2042966012","https://openalex.org/W2046436885","https://openalex.org/W2046975748","https://openalex.org/W2052888479","https://openalex.org/W2053986024","https://openalex.org/W2054766372","https://openalex.org/W2060159282","https://openalex.org/W2071886810","https://openalex.org/W2112736257","https://openalex.org/W2122966599","https://openalex.org/W2126209209","https://openalex.org/W2129142192","https://openalex.org/W2130519984","https://openalex.org/W2142210784","https://openalex.org/W2149293266","https://openalex.org/W2160220344","https://openalex.org/W2165766451","https://openalex.org/W2166578450","https://openalex.org/W2340541605","https://openalex.org/W2549866415","https://openalex.org/W2552239609","https://openalex.org/W2594760764","https://openalex.org/W2607478799","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2941904294","https://openalex.org/W2946959590","https://openalex.org/W2950130089","https://openalex.org/W2953036547","https://openalex.org/W2963203059","https://openalex.org/W2963539886","https://openalex.org/W2964062785","https://openalex.org/W2964064460","https://openalex.org/W2971791303","https://openalex.org/W2981407399","https://openalex.org/W2999584269","https://openalex.org/W3000510284","https://openalex.org/W3011106694","https://openalex.org/W3030809477","https://openalex.org/W3088225114","https://openalex.org/W4242349375","https://openalex.org/W4247689285","https://openalex.org/W4253682120","https://openalex.org/W4288400169","https://openalex.org/W4298550759","https://openalex.org/W4300302225","https://openalex.org/W4304979937","https://openalex.org/W4318049353","https://openalex.org/W6633799571"],"related_works":["https://openalex.org/W4297942051","https://openalex.org/W2614584191","https://openalex.org/W2951906341","https://openalex.org/W2119910493","https://openalex.org/W4302394113","https://openalex.org/W1980917265","https://openalex.org/W1483532407","https://openalex.org/W2963864024","https://openalex.org/W2017364159","https://openalex.org/W2601322300"],"abstract_inverted_index":{"We":[0,14,96,157],"build":[1],"on":[2,81],"recent":[3],"work":[4],"of":[5,23,37,41,92,110,153,168,178],"Yeats,":[6],"Courtiel,":[7],"and":[8,27,48,65,73,108,127,145,149,161,176],"others":[9],"involving":[10],"connected":[11,43,102],"chord":[12,44,82,175],"diagrams.":[13],"first":[15],"derive":[16],"from":[17],"a":[18,21,69,98,111,150,163,172],"Hopf-algebraic":[19],"foundation":[20],"class":[22],"tree-like":[24],"functional":[25],"equations":[26,56],"prove":[28],"that":[29],"they":[30],"are":[31],"solved":[32],"by":[33,141,159],"weighted":[34,42],"generating":[35],"functions":[36],"two":[38],"different":[39],"subsets":[40],"diagrams:":[45],"arbitrary":[46],"diagrams":[47,49,83,104,167,177],"forbidding":[50,142],"so-called":[51],"top":[52],"cycle":[53],"subdiagrams.":[54],"These":[55],"generalize":[57],"the":[58,90,118],"classic":[59],"specification":[60],"for":[61],"increasing":[62],"ordered":[63],"trees":[64],"their":[66],"solution":[67],"uses":[68],"novel":[70,93],"decomposition,":[71],"simplifying":[72],"generalizing":[74],"previous":[75],"results.":[76],"The":[77],"resulting":[78],"tree":[79],"perspective":[80],"leads":[84],"to":[85,122,132],"new":[86,133],"enumerative":[87],"insights":[88],"through":[89],"study":[91],"diagram":[94,138],"classes.":[95],"present":[97],"recursive":[99],"bijection":[100,165],"between":[101,137,166],"top-cycle-free":[103],"with":[105,113,171],"\\(n\\)":[106,170],"chords":[107],"triangulations":[109],"disk":[112],"\\(n+1\\)":[114],"vertices,":[115],"thereby":[116],"counting":[117],"former.":[119],"This":[120],"connects":[121],"combinatorial":[123,155,192,196],"maps,":[124,197],"Catalan":[125,199],"intervals,":[126],"uniquely":[128,201],"sorted":[129,202],"permutations,":[130],"leading":[131],"conjectured":[134],"bijective":[135],"relationships":[136],"classes":[139],"defined":[140],"graphical":[143],"subdiagrams":[144],"imposing":[146],"connectedness":[147],"properties":[148],"rich":[151],"variety":[152],"other":[154],"objects.":[156],"conclude":[158],"exhibiting":[160],"studying":[162],"direct":[164],"size":[169,179],"single":[173],"terminal":[174],"\\(n-1\\).Mathematics":[180],"Subject":[181],"Classifications:":[182],"05A05,":[183],"05A10,":[184],"05A15,":[185],"05A18,":[186],"05A19Keywords:":[187],"Chord":[188],"diagrams,":[189],"perfect":[190],"matchings,":[191],"classes,":[193],"pattern":[194],"avoidance,":[195],"triangulations,":[198],"posets,":[200],"permutations":[203]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2021-04-13T00:00:00"}
