{"id":"https://openalex.org/W1655265973","doi":"https://doi.org/10.37236/5410","title":"Growth Rates of Groups associated with Face 2-Coloured Triangulations and Directed Eulerian Digraphs on the Sphere","display_name":"Growth Rates of Groups associated with Face 2-Coloured Triangulations and Directed Eulerian Digraphs on the Sphere","publication_year":2016,"publication_date":"2016-03-18","ids":{"openalex":"https://openalex.org/W1655265973","doi":"https://doi.org/10.37236/5410","mag":"1655265973"},"language":"en","primary_location":{"id":"doi:10.37236/5410","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5410","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p51/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p51/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065865197","display_name":"Thomas A. McCourt","orcid":null},"institutions":[{"id":"https://openalex.org/I897542642","display_name":"University of Plymouth","ror":"https://ror.org/008n7pv89","country_code":"GB","type":"education","lineage":["https://openalex.org/I897542642"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Thomas A. McCourt","raw_affiliation_strings":["Plymouth University","#N#Plymouth University#N#"],"affiliations":[{"raw_affiliation_string":"Plymouth University","institution_ids":["https://openalex.org/I897542642"]},{"raw_affiliation_string":"#N#Plymouth University#N#","institution_ids":["https://openalex.org/I897542642"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065865197"],"corresponding_institution_ids":["https://openalex.org/I897542642"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00197749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9959999918937683,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/combinatorics","display_name":"Combinatorics","score":0.7882890701293945},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6855589747428894},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6252240538597107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5320815443992615},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.506622850894928},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4480500817298889},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2925623655319214},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19991305470466614},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1817423701286316},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06312191486358643}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7882890701293945},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6855589747428894},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6252240538597107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5320815443992615},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.506622850894928},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4480500817298889},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2925623655319214},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19991305470466614},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1817423701286316},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06312191486358643}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/5410","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5410","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p51/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1408.2984","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.2984","pdf_url":"https://arxiv.org/pdf/1408.2984","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":"mag:1655265973","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1408.2984v4","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1408.2984","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1408.2984","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:10.37236/5410","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5410","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p51/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1655265973.pdf","grobid_xml":"https://content.openalex.org/works/W1655265973.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W265291222","https://openalex.org/W1540892394","https://openalex.org/W1971079746","https://openalex.org/W1978288875","https://openalex.org/W1980948271","https://openalex.org/W2004698389","https://openalex.org/W2009331596","https://openalex.org/W2016631456","https://openalex.org/W2024989372","https://openalex.org/W2028747048","https://openalex.org/W2030009010","https://openalex.org/W2065463969","https://openalex.org/W2111425983","https://openalex.org/W2132345770","https://openalex.org/W2736849238","https://openalex.org/W2799004609","https://openalex.org/W2964090757","https://openalex.org/W3134545872","https://openalex.org/W6657409826","https://openalex.org/W6676863361","https://openalex.org/W6679217458","https://openalex.org/W6684556191"],"related_works":["https://openalex.org/W2963780827","https://openalex.org/W2952516074","https://openalex.org/W3102686903","https://openalex.org/W3106412376","https://openalex.org/W2101592675","https://openalex.org/W1973062853","https://openalex.org/W2952199243","https://openalex.org/W2002604535","https://openalex.org/W2166171115","https://openalex.org/W1513441663","https://openalex.org/W2020641847","https://openalex.org/W2952121958","https://openalex.org/W2140117897","https://openalex.org/W2291891535","https://openalex.org/W2015584643","https://openalex.org/W2184152084","https://openalex.org/W2103638036","https://openalex.org/W3101696536","https://openalex.org/W2951696486","https://openalex.org/W2332891270"],"abstract_inverted_index":{"Let":[0,83],"$\\mathcal{G}$":[1],"be":[2,47,85],"a":[3,65,107],"properly":[4,93],"face":[5,94],"$2$-coloured":[6],"(say":[7],"black":[8,51],"and":[9,41,132],"white)":[10],"piecewise-linear":[11],"triangulation":[12,108],"of":[13,80,89,101,115],"the":[14,21,27,58,77,81,86,124],"sphere":[15],"with":[16,30,37,98],"vertex":[17],"set":[18,28],"$V$.":[19],"Consider":[20],"abelian":[22,67,118],"group":[23,44,79,127],"$\\mathcal{A}_W$":[24],"generated":[25],"by":[26],"$V$,":[29],"relations":[31],"$r+c+s=0$":[32],"for":[33,135],"all":[34,92],"white":[35],"triangles":[36,100],"vertices":[38],"$r$,":[39],"$c$":[40],"$s$.":[42],"The":[43],"$\\mathcal{A}_B$":[45],"can":[46],"defined":[48],"similarly,":[49],"using":[50],"triangles.":[52],"These":[53],"groups":[54,120],"are":[55,121],"related":[56],"in":[57],"following":[59],"manner":[60],"$\\mathcal{A}_W\\cong\\mathcal{A}_B\\cong\\mathbb{Z}\\oplus\\mathbb{Z}\\oplus\\mathcal{C}$":[61],"where":[62],"$\\mathcal{C}$":[63,72,90],"is":[64,73],"finite":[66,69],"group.The":[68],"torsion":[70],"subgroup":[71],"referred":[74],"to":[75,109,123],"as":[76],"canonical":[78,126],"triangulation.":[82],"$m_t$":[84],"maximal":[87],"order":[88],"over":[91],"2-coloured":[95],"spherical":[96,113],"triangulations":[97],"$t$":[99],"each":[102],"colour.":[103],"By":[104],"relating":[105],"such":[106],"certain":[110],"directed":[111],"Eulerian":[112],"embeddings":[114],"digraphs":[116],"whose":[117],"sand-pile":[119],"isomorphic":[122],"triangulation's":[125],"we":[128],"provide":[129],"improved":[130],"upper":[131],"lower":[133],"bounds":[134],"$\\lim":[136],"\\sup_{t\\rightarrow\\infty}(m_t)^{1/t}$.":[137]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
