{"id":"https://openalex.org/W2993861634","doi":"https://doi.org/10.1007/s00454-019-00157-z","title":"Flip-Connectivity of Triangulations of the Product of a Tetrahedron and Simplex","display_name":"Flip-Connectivity of Triangulations of the Product of a Tetrahedron and Simplex","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2993861634","doi":"https://doi.org/10.1007/s00454-019-00157-z","mag":"2993861634"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-019-00157-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-019-00157-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-019-00157-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-019-00157-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110628567","display_name":"Gaku Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gaku Liu","raw_affiliation_strings":["Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Leipzig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2212-9919","affiliations":[{"raw_affiliation_string":"Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110628567"],"corresponding_institution_ids":["https://openalex.org/I4210091327"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.31451356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"63","issue":"1","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9980999827384949,"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":0.9980999827384949,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.996399998664856,"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":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.8704259395599365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8297804594039917},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8212407827377319},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.8063560128211975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6816853880882263},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5866518616676331},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5588692426681519},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45167723298072815},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42277365922927856},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20299237966537476},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13979065418243408}],"concepts":[{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.8704259395599365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8297804594039917},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8212407827377319},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.8063560128211975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6816853880882263},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5866518616676331},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5588692426681519},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45167723298072815},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42277365922927856},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20299237966537476},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13979065418243408},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-019-00157-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-019-00157-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-019-00157-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-019-00157-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-019-00157-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-019-00157-z.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3526151021","display_name":null,"funder_award_id":"1122374","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2993861634.pdf","grobid_xml":"https://content.openalex.org/works/W2993861634.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W116735976","https://openalex.org/W1583624126","https://openalex.org/W1782695725","https://openalex.org/W1961766557","https://openalex.org/W1975481860","https://openalex.org/W1977415556","https://openalex.org/W2012741742","https://openalex.org/W2032234362","https://openalex.org/W2041411907","https://openalex.org/W2055354724","https://openalex.org/W2063128973","https://openalex.org/W2081659888","https://openalex.org/W2404691076","https://openalex.org/W2963001177","https://openalex.org/W3037914599","https://openalex.org/W3102279813","https://openalex.org/W4206077821","https://openalex.org/W4244115379","https://openalex.org/W4246108584","https://openalex.org/W4320523390","https://openalex.org/W6601658864"],"related_works":["https://openalex.org/W1642182499","https://openalex.org/W2804594029","https://openalex.org/W2993861634","https://openalex.org/W1972907943","https://openalex.org/W2770920891","https://openalex.org/W3092318790","https://openalex.org/W2972087021","https://openalex.org/W2404691076","https://openalex.org/W2087158646","https://openalex.org/W894129231"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"flip":[2],"is":[3,33,55,74,83,92,100,116,123],"a":[4,11,18,69,84,124],"minimal":[5],"move":[6],"between":[7],"two":[8,59,72],"triangulations":[9,16,67],"of":[10,15,17,41,58,66,68,71,80,97,120],"polytope.":[12],"The":[13],"set":[14,65],"polytope":[19],"was":[20],"shown":[21],"by":[22,29,76],"Santos":[23,61],"to":[24,37],"not":[25,93],"always":[26],"be":[27],"connected":[28,75,94,117],"flips,":[30],"and":[31,102],"it":[32,45,91,115],"an":[34],"interesting":[35],"problem":[36],"find":[38],"large":[39,107],"classes":[40],"polytopes":[42],"for":[43],"which":[44,50],"is.":[46],"One":[47],"such":[48],"class":[49],"has":[51,105],"received":[52],"considerable":[53],"attention":[54],"the":[56,64,81,87,98,103,121],"product":[57,70],"simplices.":[60],"proved":[62],"that":[63,90,114],"simplices":[73,82,99,122],"flips":[77],"when":[78,95,118],"one":[79,96,119],"triangle.":[85],"However,":[86],"author":[88],"showed":[89],"four-dimensional":[101],"other":[104],"very":[106],"dimension.":[108],"In":[109],"this":[110],"paper":[111],"we":[112],"show":[113],"tetrahedron,":[125],"thereby":[126],"extending":[127],"Santos\u2019s":[128],"result":[129],"as":[130,132],"far":[131],"possible.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}