{"id":"https://openalex.org/W4385302314","doi":"https://doi.org/10.1090/mcom/3886","title":"Coupler curves of moving graphs and counting realizations of rigid graphs","display_name":"Coupler curves of moving graphs and counting realizations of rigid graphs","publication_year":2023,"publication_date":"2023-07-27","ids":{"openalex":"https://openalex.org/W4385302314","doi":"https://doi.org/10.1090/mcom/3886"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3886","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3886","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04735714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038715886","display_name":"Georg Grasegger","orcid":"https://orcid.org/0000-0001-7421-8115"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Georg Grasegger","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Stra\u00c3\u009fe 69, 4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Stra\u00c3\u009fe 69, 4040 Linz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003791096","display_name":"Boulos El Hilany","orcid":"https://orcid.org/0000-0002-9654-906X"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Boulos El Hilany","raw_affiliation_strings":["Institut f\u00c3\u00bcr Analysis und Algebra, TU Braunschweig, Universit\u00c3\u00a4tsplatz 2, 38106 Braunschweig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Analysis und Algebra, TU Braunschweig, Universit\u00c3\u00a4tsplatz 2, 38106 Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041212379","display_name":"Niels Lubbes","orcid":"https://orcid.org/0000-0001-7018-2725"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Niels Lubbes","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Stra\u00c3\u009fe 69, 4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Stra\u00c3\u009fe 69, 4040 Linz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038715886"],"corresponding_institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"],"apc_list":null,"apc_paid":null,"fwci":0.5871,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63535474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"93","issue":"345","first_page":"459","last_page":"504"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9990000128746033,"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":0.9990000128746033,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9965000152587891,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9950000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8642795085906982},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7006580233573914},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5987164378166199},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.43873587250709534},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42526954412460327},{"id":"https://openalex.org/keywords/revolute-joint","display_name":"Revolute joint","score":0.4231649339199066},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3952983021736145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23319080471992493}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8642795085906982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7006580233573914},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5987164378166199},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.43873587250709534},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42526954412460327},{"id":"https://openalex.org/C5643039","wikidata":"https://www.wikidata.org/wiki/Q3819341","display_name":"Revolute joint","level":3,"score":0.4231649339199066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3952983021736145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23319080471992493},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3886","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3886","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04735714v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04735714","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2023, 93 (345), pp.459-504. &#x27E8;10.1090/mcom/3886&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04735714v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04735714","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 2023, 93 (345), pp.459-504. &#x27E8;10.1090/mcom/3886&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7099999785423279,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2502472462","display_name":"Realizations of Rigid Graphs","funder_award_id":"P31888","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4589013483","display_name":"Trajectories of motions","funder_award_id":"P33003","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W56381843","https://openalex.org/W170014338","https://openalex.org/W1917545407","https://openalex.org/W2013407568","https://openalex.org/W2026588045","https://openalex.org/W2027524385","https://openalex.org/W2037009986","https://openalex.org/W2082755095","https://openalex.org/W2098066887","https://openalex.org/W2100909061","https://openalex.org/W2121403868","https://openalex.org/W2139834426","https://openalex.org/W2319466955","https://openalex.org/W2581659641","https://openalex.org/W2766037965","https://openalex.org/W2784208434","https://openalex.org/W2902145203","https://openalex.org/W3020003842","https://openalex.org/W3032242654","https://openalex.org/W3043945154","https://openalex.org/W3093733732","https://openalex.org/W3098923886","https://openalex.org/W3101761638","https://openalex.org/W3102833916","https://openalex.org/W3134502299","https://openalex.org/W3137636070","https://openalex.org/W4230260990","https://openalex.org/W4241140300","https://openalex.org/W4248269519","https://openalex.org/W4250817735","https://openalex.org/W4385302314","https://openalex.org/W6602341653"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2883550785","https://openalex.org/W2890977713","https://openalex.org/W1980749193","https://openalex.org/W2123089778","https://openalex.org/W2899776278","https://openalex.org/W2790463165","https://openalex.org/W2116626317","https://openalex.org/W2065877964","https://openalex.org/W2051473190"],"abstract_inverted_index":{"A":[0,74],"calligraph":[1,41,49],"is":[2,42,99,112],"a":[3,36,53,100,115],"graph":[4],"that":[5,76,107],"for":[6,93,135],"almost":[7,94],"all":[8,95],"edge":[9,25,96],"length":[10,97],"assignments":[11],"moves":[12],"with":[13],"one":[14],"degree":[15],"of":[16,35,39,56,67,70,102,110,119,138,147],"freedom":[17],"in":[18],"the":[19,28,40,62,71,91,120],"plane,":[20],"if":[21],"we":[22,50,130,144],"fix":[23],"an":[24,128,132],"and":[26,64,80,140],"consider":[27],"vertices":[29],"as":[30],"revolute":[31],"joints.":[32],"The":[33],"trajectory":[34],"distinguished":[37],"vertex":[38],"called":[43],"its":[44],"coupler":[45,72,148],"curve.":[46,73],"To":[47],"each":[48],"uniquely":[51],"assign":[52],"vector":[54,60],"consisting":[55],"three":[57],"integers.":[58],"This":[59],"bounds":[61],"degrees":[63],"geometric":[65],"genera":[66],"irreducible":[68],"components":[69],"graph,":[75],"up":[77],"to":[78,114,123],"rotations":[79],"translations":[81],"admits":[82],"finitely":[83],"many,":[84],"but":[85],"at":[86],"least":[87],"two,":[88],"realizations":[89,111,143],"into":[90],"plane":[92],"assignments,":[98],"union":[101],"two":[103,125],"calligraphs.":[104,126],"We":[105],"show":[106],"this":[108],"number":[109],"equal":[113],"certain":[116],"inner":[117],"product":[118],"vectors":[121],"associated":[122],"these":[124],"As":[127],"application":[129],"obtain":[131],"improved":[133],"algorithm":[134],"counting":[136,142],"numbers":[137],"realizations,":[139],"by":[141],"characterize":[145],"invariants":[146],"curves.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
