{"id":"https://openalex.org/W3178234669","doi":"https://doi.org/10.1007/s00454-023-00546-5","title":"Braced Triangulations and Rigidity","display_name":"Braced Triangulations and Rigidity","publication_year":2023,"publication_date":"2023-08-19","ids":{"openalex":"https://openalex.org/W3178234669","doi":"https://doi.org/10.1007/s00454-023-00546-5","mag":"3178234669"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-023-00546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00546-5.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 &amp; 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/s00454-023-00546-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054290320","display_name":"James Cruickshank","orcid":"https://orcid.org/0000-0003-4731-9302"},"institutions":[{"id":"https://openalex.org/I188760350","display_name":"Ollscoil na Gaillimhe \u2013 University of Galway","ror":"https://ror.org/03bea9k73","country_code":"IE","type":"education","lineage":["https://openalex.org/I188760350"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"James Cruickshank","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland"],"raw_orcid":"https://orcid.org/0000-0003-4731-9302","affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland","institution_ids":["https://openalex.org/I188760350"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014405567","display_name":"Eleftherios Kastis","orcid":"https://orcid.org/0000-0002-9405-723X"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Eleftherios Kastis","raw_affiliation_strings":["Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041310419","display_name":"Derek Kitson","orcid":"https://orcid.org/0000-0003-1608-6139"},"institutions":[{"id":"https://openalex.org/I4387155487","display_name":"Mary Immaculate College","ror":"https://ror.org/009q3yg92","country_code":null,"type":"education","lineage":["https://openalex.org/I4387155487"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Derek Kitson","raw_affiliation_strings":["Department of Mathematics and Computer Studies, Mary Immaculate College, Thurles, Co. Tipperary, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Studies, Mary Immaculate College, Thurles, Co. Tipperary, Ireland","institution_ids":["https://openalex.org/I4387155487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054659172","display_name":"Bernd Schulze","orcid":"https://orcid.org/0000-0002-6272-4296"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bernd Schulze","raw_affiliation_strings":["Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK","institution_ids":["https://openalex.org/I67415387"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054290320"],"corresponding_institution_ids":["https://openalex.org/I188760350"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4943,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66027237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"71","issue":"4","first_page":"1238","last_page":"1275"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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":0.9993000030517578,"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/T11870","display_name":"Structural Analysis and Optimization","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9926000237464905,"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/algorithm","display_name":"Algorithm","score":0.5849080681800842},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.4462580978870392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43763527274131775},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4336041212081909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40380722284317017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38125625252723694},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1183098554611206}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5849080681800842},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4462580978870392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43763527274131775},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4336041212081909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40380722284317017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38125625252723694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1183098554611206}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-023-00546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00546-5.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 &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lancs.ac.uk:198554","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.lancs.ac.uk/id/eprint/198554/1/Braced_Plane_Triangulations.pdf","source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"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":"PeerReviewed"}],"best_oa_location":{"id":"doi:10.1007/s00454-023-00546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-023-00546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-023-00546-5.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 &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3119524140","display_name":null,"funder_award_id":"EP/S00940X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320318630","display_name":"Irish Research eLibrary","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3178234669.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W133608936","https://openalex.org/W258977970","https://openalex.org/W1672415299","https://openalex.org/W1860988242","https://openalex.org/W2016157352","https://openalex.org/W2032955869","https://openalex.org/W2035770249","https://openalex.org/W2086459036","https://openalex.org/W2900668458","https://openalex.org/W2963074634","https://openalex.org/W2963642462","https://openalex.org/W2964023517","https://openalex.org/W3008572889","https://openalex.org/W3040786338","https://openalex.org/W3049755108","https://openalex.org/W3103336111","https://openalex.org/W3137414324","https://openalex.org/W4251519580","https://openalex.org/W4252017042"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Abstract":[0],"We":[1,25],"consider":[2],"the":[3,56,73,89],"problem":[4],"of":[5,14,21,39,59,91,132],"finding":[6],"an":[7,36],"inductive":[8,37],"construction,":[9],"based":[10],"on":[11,135],"vertex":[12],"splitting,":[13],"triangulated":[15],"spheres":[16],"with":[17,41,63],"a":[18,53,60,115,130],"fixed":[19],"number":[20],"additional":[22],"edges":[23],"(braces).":[24],"show":[26,99],"that":[27,66,75,100],"for":[28,55],"any":[29],"positive":[30],"integer":[31],"b":[32,42,64,70],"there":[33],"is":[34,67],"such":[35],"construction":[38],"triangulations":[40,103],"braces,":[43],"having":[44],"finitely":[45],"many":[46],"base":[47,61,92],"graphs.":[48],"In":[49,72],"particular":[50],"we":[51,87,98],"establish":[52],"bound":[54],"maximum":[57],"size":[58],"graph":[62],"braces":[65],"linear":[68],"in":[69,108,117],".":[71,147],"case":[74],"$$b=1$$":[76],"<mml:math":[77,120,138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[78,121,139],"<mml:mrow>":[79,123,141],"<mml:mi>b</mml:mi>":[80],"<mml:mo>=</mml:mo>":[81],"<mml:mn>1</mml:mn>":[82],"</mml:mrow>":[83,125,143],"</mml:math>":[84,128,146],"or":[85],"2":[86],"determine":[88],"list":[90],"graphs":[93],"explicitly.":[94],"Using":[95],"these":[96],"results":[97],"doubly":[101],"braced":[102],"are":[104],"(generically)":[105],"minimally":[106],"rigid":[107],"two":[109],"distinct":[110],"geometric":[111],"contexts":[112],"arising":[113],"from":[114],"hypercylinder":[116],"$$\\mathbb":[118,136],"{R}^4$$":[119],"<mml:msup>":[122,140],"<mml:mi>R</mml:mi>":[124,142],"<mml:mn>4</mml:mn>":[126],"</mml:msup>":[127,145],"and":[129],"class":[131],"mixed":[133],"norms":[134],"{R}^3$$":[137],"<mml:mn>3</mml:mn>":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-01-23T23:20:30.427331","created_date":"2025-10-10T00:00:00"}