{"id":"https://openalex.org/W2100909061","doi":"https://doi.org/10.1007/978-3-642-11805-0_19","title":"Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs","display_name":"Algebraic Methods for Counting Euclidean Embeddings of Rigid Graphs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2100909061","doi":"https://doi.org/10.1007/978-3-642-11805-0_19","mag":"2100909061"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-11805-0_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-11805-0_19","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-11805-0_19.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-11805-0_19.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210106545","display_name":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106545"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elias P. Tsigaridas","raw_affiliation_strings":["INRIA M\u00e9diterran\u00e9e, Sophia-Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA M\u00e9diterran\u00e9e, Sophia-Antipolis, France","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078214509","display_name":"Antonios Varvitsiotis","orcid":"https://orcid.org/0000-0002-9658-6469"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Antonios E. Varvitsiotis","raw_affiliation_strings":["CWI, Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CWI, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.2649,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.7814992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"195","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9990000128746033,"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":0.9990000128746033,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9861000180244446,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7211554050445557},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6977108716964722},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6200825572013855},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6200165152549744},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6150684356689453},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5314202308654785},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5168505311012268},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5099352598190308},{"id":"https://openalex.org/keywords/mixed-volume","display_name":"Mixed volume","score":0.490418404340744},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48917606472969055},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45848602056503296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4021919369697571},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2563713788986206},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.22183462977409363},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.18320512771606445},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06129050254821777}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7211554050445557},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6977108716964722},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6200825572013855},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6200165152549744},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6150684356689453},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5314202308654785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5168505311012268},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5099352598190308},{"id":"https://openalex.org/C44550424","wikidata":"https://www.wikidata.org/wiki/Q4424496","display_name":"Mixed volume","level":5,"score":0.490418404340744},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48917606472969055},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45848602056503296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4021919369697571},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2563713788986206},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.22183462977409363},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18320512771606445},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06129050254821777},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":5,"locations":[{"id":"doi:10.1007/978-3-642-11805-0_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-11805-0_19","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-11805-0_19.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:cwi:oai:cwi.nl:14983","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/14983","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencepaper"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.9066","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.9066","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0906.1437v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.249.1969","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.1969","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0906.1437v1.pdf","raw_type":"text"},{"id":"pmh:oai:gdea.informatik.uni-koeln.de:1084","is_oa":false,"landing_page_url":"http://gdea.informatik.uni-koeln.de/1084/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196197","display_name":"gdea - Graph Drawing E-print Archive (GDEA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":{"id":"doi:10.1007/978-3-642-11805-0_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-642-11805-0_19","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-642-11805-0_19.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4510835956","display_name":"Decompositions Tensorielles et applications","funder_award_id":"ANR-06-BLAN-0074","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320323149","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2100909061.pdf","grobid_xml":"https://content.openalex.org/works/W2100909061.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W133608936","https://openalex.org/W1976673195","https://openalex.org/W2011055896","https://openalex.org/W2026588045","https://openalex.org/W2037009986","https://openalex.org/W2055810284","https://openalex.org/W2066130115","https://openalex.org/W2074906705","https://openalex.org/W2093547815","https://openalex.org/W2143023483","https://openalex.org/W2153992422","https://openalex.org/W2170272663","https://openalex.org/W4235640392","https://openalex.org/W4253253982"],"related_works":["https://openalex.org/W2289965647","https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2145396827","https://openalex.org/W2279239548","https://openalex.org/W4294294347","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W164473625","https://openalex.org/W2105228010"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}