{"id":"https://openalex.org/W2901138657","doi":"https://doi.org/10.37236/8394","title":"Balanced Triangulations on few Vertices and an Implementation of Cross-Flips","display_name":"Balanced Triangulations on few Vertices and an Implementation of Cross-Flips","publication_year":2019,"publication_date":"2019-09-27","ids":{"openalex":"https://openalex.org/W2901138657","doi":"https://doi.org/10.37236/8394","mag":"2901138657"},"language":"en","primary_location":{"id":"doi:10.37236/8394","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8394","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p61/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/v26i3p61/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018528607","display_name":"Lorenzo Venturello","orcid":"https://orcid.org/0000-0002-6797-5270"},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lorenzo Venturello","raw_affiliation_strings":["Universit\u00e4t Osnabr\u00fcck"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Osnabr\u00fcck","institution_ids":["https://openalex.org/I170658231"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018528607"],"corresponding_institution_ids":["https://openalex.org/I170658231"],"apc_list":null,"apc_paid":null,"fwci":0.2,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50284322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9983999729156494,"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":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.745427131652832},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7365249991416931},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5852745175361633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5582926273345947},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.521072506904602},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4632861018180847},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4523821175098419},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1003541648387909}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.745427131652832},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7365249991416931},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5852745175361633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5582926273345947},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.521072506904602},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4632861018180847},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4523821175098419},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1003541648387909},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8394","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8394","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p61/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:1811.10271","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.10271","pdf_url":"https://arxiv.org/pdf/1811.10271","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:2901138657","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1811.10271","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.1811.10271","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.10271","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:10.37236/8394","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8394","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p61/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":[{"display_name":"Sustainable cities and communities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5813364639","display_name":null,"funder_award_id":"GRK-1916","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2901138657.pdf","grobid_xml":"https://content.openalex.org/works/W2901138657.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W206167714","https://openalex.org/W1515761639","https://openalex.org/W1977811461","https://openalex.org/W2125647258","https://openalex.org/W2147405597","https://openalex.org/W2165125983","https://openalex.org/W2585949860","https://openalex.org/W2911463656","https://openalex.org/W2962739814","https://openalex.org/W2963260537","https://openalex.org/W2963905120","https://openalex.org/W2963918064","https://openalex.org/W2963980320","https://openalex.org/W2969180071","https://openalex.org/W3098716176"],"related_works":["https://openalex.org/W3000131309","https://openalex.org/W2207465479","https://openalex.org/W2909842178","https://openalex.org/W3118536607","https://openalex.org/W986668203","https://openalex.org/W2893498999","https://openalex.org/W2952958025","https://openalex.org/W1969801783","https://openalex.org/W1785367054","https://openalex.org/W2019017480","https://openalex.org/W2963884553","https://openalex.org/W1978430562","https://openalex.org/W2952634096","https://openalex.org/W1967167259","https://openalex.org/W2950494490","https://openalex.org/W2950177555","https://openalex.org/W3032809983","https://openalex.org/W2155123294","https://openalex.org/W1657864480","https://openalex.org/W3015664627"],"abstract_inverted_index":{"A":[0],"$d$-dimensional":[1],"simplicial":[2],"complex":[3],"is":[4,10],"balanced":[5,34,45,66,80],"if":[6],"the":[7,48,53,58,83],"underlying":[8],"graph":[9],"$(d+1)$-colorable.":[11],"We":[12],"present":[13],"an":[14],"implementation":[15],"of":[16,20,47,52,57,68,82],"cross-flips,":[17],"a":[18,38,42],"set":[19],"local":[21],"moves":[22],"introduced":[23],"by":[24],"Izmestiev,":[25],"Klee":[26],"and":[27,56,70,88],"Novik":[28],"which":[29],"connect":[30],"any":[31],"two":[32],"PL-homeomorphic":[33],"combinatorial":[35],"manifolds.":[36],"As":[37],"result":[39],"we":[40,77],"exhibit":[41],"vertex":[43,92],"minimal":[44],"triangulation":[46],"real":[49,59],"projective":[50,60],"plane,":[51],"dunce":[54],"hat":[55],"space,":[61],"as":[62,64],"well":[63],"several":[65],"triangulations":[67,81],"surfaces":[69],"3-manifolds":[71],"on":[72],"few":[73],"vertices.":[74],"In":[75],"particular":[76],"construct":[78],"small":[79],"3-sphere":[84],"that":[85],"are":[86],"non-shellable":[87],"shellable":[89],"but":[90],"not":[91],"decomposable.":[93]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
