{"id":"https://openalex.org/W3078437961","doi":"https://doi.org/10.1007/s00454-020-00234-8","title":"The Combinatorial Geometry of Stresses in Frameworks","display_name":"The Combinatorial Geometry of Stresses in Frameworks","publication_year":2020,"publication_date":"2020-08-18","ids":{"openalex":"https://openalex.org/W3078437961","doi":"https://doi.org/10.1007/s00454-020-00234-8","mag":"3078437961"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-020-00234-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00234-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00234-8.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/s00454-020-00234-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042036894","display_name":"Oleg Karpenkov","orcid":"https://orcid.org/0000-0002-3358-6998"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Oleg Karpenkov","raw_affiliation_strings":["University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, UK","University of Liverpool, Mathematical Sciences Building, Liverpool, L69 7ZL, UK"],"raw_orcid":"https://orcid.org/0000-0002-3358-6998","affiliations":[{"raw_affiliation_string":"University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"University of Liverpool, Mathematical Sciences Building, Liverpool, L69 7ZL, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042036894"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.1464,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48882353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"65","issue":"1","first_page":"43","last_page":"89"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9998000264167786,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9635000228881836,"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/mathematics","display_name":"Mathematics","score":0.7407525777816772},{"id":"https://openalex.org/keywords/tensegrity","display_name":"Tensegrity","score":0.6481592655181885},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5629417896270752},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5572021007537842},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5496033430099487},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.5297974944114685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35406655073165894},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.342548131942749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33102113008499146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7407525777816772},{"id":"https://openalex.org/C182950735","wikidata":"https://www.wikidata.org/wiki/Q1930978","display_name":"Tensegrity","level":2,"score":0.6481592655181885},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5629417896270752},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5572021007537842},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5496033430099487},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5297974944114685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35406655073165894},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.342548131942749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33102113008499146},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-020-00234-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00234-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00234-8.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"}],"best_oa_location":{"id":"doi:10.1007/s00454-020-00234-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-020-00234-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-020-00234-8.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/G1500779617","display_name":null,"funder_award_id":"EP/N014499/1 (LCMH)","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4745889958","display_name":null,"funder_award_id":"EP/N034333/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G506567556","display_name":null,"funder_award_id":"Grant EP/N014499/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7173905922","display_name":"EPSRC Centre for New Mathematical Sciences Capabilities for Healthcare Technologies","funder_award_id":"EP/N014499/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8672101347","display_name":null,"funder_award_id":"EP/N014499/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3078437961.pdf","grobid_xml":"https://content.openalex.org/works/W3078437961.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W43500862","https://openalex.org/W136053314","https://openalex.org/W258977970","https://openalex.org/W563320997","https://openalex.org/W634394376","https://openalex.org/W1482924361","https://openalex.org/W1530933630","https://openalex.org/W1543767267","https://openalex.org/W1604266498","https://openalex.org/W1626064980","https://openalex.org/W1945231261","https://openalex.org/W1971255824","https://openalex.org/W1978514943","https://openalex.org/W1985907665","https://openalex.org/W2010767803","https://openalex.org/W2015745944","https://openalex.org/W2019867625","https://openalex.org/W2032955869","https://openalex.org/W2046512615","https://openalex.org/W2068418846","https://openalex.org/W2070613680","https://openalex.org/W2076545664","https://openalex.org/W2078507839","https://openalex.org/W2093752739","https://openalex.org/W2104990897","https://openalex.org/W2113001921","https://openalex.org/W2113396371","https://openalex.org/W2118003507","https://openalex.org/W2480279707","https://openalex.org/W2809700945","https://openalex.org/W2913234940","https://openalex.org/W2914659449","https://openalex.org/W2953304270","https://openalex.org/W2962883236","https://openalex.org/W3103336111","https://openalex.org/W3141809287","https://openalex.org/W4210394880","https://openalex.org/W4230663566","https://openalex.org/W4252017042","https://openalex.org/W6600146248","https://openalex.org/W6697549010"],"related_works":["https://openalex.org/W227057133","https://openalex.org/W2480265123","https://openalex.org/W2345199500","https://openalex.org/W2090167696","https://openalex.org/W2382222318","https://openalex.org/W3142983119","https://openalex.org/W2040728928","https://openalex.org/W2902808963","https://openalex.org/W2727566482","https://openalex.org/W2802954506"],"abstract_inverted_index":{"Abstract":[0],"Consider":[1],"a":[2,5,18,45],"realization":[3,43],"of":[4,30,83],"graph":[6,32,75],"in":[7,69,81],"the":[8,31,33,42,53,70],"space":[9],"with":[10],"straight":[11],"segments":[12],"representing":[13],"edges.":[14],"Let":[15],"us":[16],"assign":[17],"stress":[19],"for":[20,67],"every":[21,28],"its":[22],"edge.":[23],"In":[24,57],"case":[25],"if":[26],"at":[27],"vertex":[29],"stresses":[34],"sum":[35],"up":[36],"to":[37],"zero,":[38],"we":[39,60,76],"say":[40],"that":[41],"is":[44],"tensegrity.":[46],"Some":[47],"realizations":[48],"possess":[49],"non-zero":[50],"tensegrities":[51,68],"while":[52],"others":[54],"do":[55],"not.":[56],"this":[58],"paper":[59],"study":[61],"necessary":[62],"and":[63],"sufficient":[64],"existence":[65],"conditions":[66,80],"plane.":[71],"For":[72],"an":[73],"arbitrary":[74],"write":[77],"down":[78],"these":[79],"terms":[82],"projective":[84],"\u201cmeet-join\u201d":[85],"operations.":[86]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
