{"id":"https://openalex.org/W2026588045","doi":"https://doi.org/10.1007/s00454-003-2902-0","title":"The Number of Embeddings of Minimally Rigid Graphs","display_name":"The Number of Embeddings of Minimally Rigid Graphs","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2026588045","doi":"https://doi.org/10.1007/s00454-003-2902-0","mag":"2026588045"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-003-2902-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2902-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2902-0.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2902-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055947023","display_name":"Ciprian S. Borcea","orcid":"https://orcid.org/0000-0002-6207-9127"},"institutions":[{"id":"https://openalex.org/I186776151","display_name":"Rider University","ror":"https://ror.org/01dgn5344","country_code":"US","type":"education","lineage":["https://openalex.org/I186776151"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ciprian Borcea","raw_affiliation_strings":["Department of Mathematics, Rider University,\nLawrenceville, NJ 08648, USA","Department of Mathematics, Rider University, Lawrenceville, NJ 08648, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rider University,\nLawrenceville, NJ 08648, USA","institution_ids":["https://openalex.org/I186776151"]},{"raw_affiliation_string":"Department of Mathematics, Rider University, Lawrenceville, NJ 08648, USA#TAB#","institution_ids":["https://openalex.org/I186776151"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008565320","display_name":"Ileana Streinu","orcid":"https://orcid.org/0000-0003-2663-2615"},"institutions":[{"id":"https://openalex.org/I202524275","display_name":"Smith College","ror":"https://ror.org/0497crr92","country_code":"US","type":"education","lineage":["https://openalex.org/I202524275"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ileana Streinu","raw_affiliation_strings":["Department of Computer Science, Smith College,\nNorthampton, MA 01063, USA","Department of Computer Science, Smith College, Northampton, MA 01063, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Smith College,\nNorthampton, MA 01063, USA","institution_ids":["https://openalex.org/I202524275"]},{"raw_affiliation_string":"Department of Computer Science, Smith College, Northampton, MA 01063, USA","institution_ids":["https://openalex.org/I202524275"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055947023"],"corresponding_institution_ids":["https://openalex.org/I186776151"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":9.6671,"has_fulltext":true,"cited_by_count":84,"citation_normalized_percentile":{"value":0.97523515,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"31","issue":"2","first_page":"287","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":1.0,"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":1.0,"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":0.9977999925613403,"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":0.983299970626831,"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/combinatorics","display_name":"Combinatorics","score":0.8120046854019165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7983001470565796},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5557903051376343},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5256717801094055},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5133994817733765},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.45978856086730957},{"id":"https://openalex.org/keywords/discrete-geometry","display_name":"Discrete geometry","score":0.4540503919124603},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4245941936969757},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3557523787021637},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2107025384902954}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8120046854019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983001470565796},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5557903051376343},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5256717801094055},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5133994817733765},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.45978856086730957},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.4540503919124603},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4245941936969757},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3557523787021637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2107025384902954},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-003-2902-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2902-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2902-0.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.smith.edu:csc_facpubs-1018","is_oa":false,"landing_page_url":"https://scholarworks.smith.edu/csc_facpubs/17","pdf_url":null,"source":{"id":"https://openalex.org/S4377196392","display_name":"Smith ScholarWorks (Smith College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202524275","host_organization_name":"Smith College","host_organization_lineage":["https://openalex.org/I202524275"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science: Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-003-2902-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2902-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2902-0.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1326814937","display_name":"RUI: Oriented Matroids and Rigidity Theory Techniques for Pseudo Triangulations, Visibility Graphs and Other Structures in Computational Geometry","funder_award_id":"0105507","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5609275544","display_name":"Computational and Algorithmic Representations of Geonetric Objects - CARGO: Folding and Unfolding Processes for Polygonal Linkages, with Applications to Robotics and Biology","funder_award_id":"0138374","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2026588045.pdf","grobid_xml":"https://content.openalex.org/works/W2026588045.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W133608936","https://openalex.org/W380075320","https://openalex.org/W1494380125","https://openalex.org/W1506823273","https://openalex.org/W1516027685","https://openalex.org/W1574151794","https://openalex.org/W1582520000","https://openalex.org/W1964602626","https://openalex.org/W1970095165","https://openalex.org/W1977438424","https://openalex.org/W1987075624","https://openalex.org/W1991581432","https://openalex.org/W2001449111","https://openalex.org/W2003885039","https://openalex.org/W2041204798","https://openalex.org/W2050728700","https://openalex.org/W2055810284","https://openalex.org/W2139834426","https://openalex.org/W2158907148","https://openalex.org/W2499989309","https://openalex.org/W2742354109","https://openalex.org/W4232452168","https://openalex.org/W4244805240","https://openalex.org/W4251345737","https://openalex.org/W4255213956","https://openalex.org/W4379390876","https://openalex.org/W6610506593"],"related_works":["https://openalex.org/W4294294347","https://openalex.org/W2145396827","https://openalex.org/W2279239548","https://openalex.org/W115379796","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2105228010","https://openalex.org/W164473625"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}