{"id":"https://openalex.org/W2055393713","doi":"https://doi.org/10.3390/sym4010143","title":"Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings","display_name":"Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings","publication_year":2012,"publication_date":"2012-02-20","ids":{"openalex":"https://openalex.org/W2055393713","doi":"https://doi.org/10.3390/sym4010143","mag":"2055393713"},"language":"en","primary_location":{"id":"doi:10.3390/sym4010143","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym4010143","pdf_url":"https://www.mdpi.com/2073-8994/4/1/143/pdf?version=1329728487","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/4/1/143/pdf?version=1329728487","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113589910","display_name":"Michael Berglund","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Berglund","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081432563","display_name":"Jason Cantarella","orcid":"https://orcid.org/0000-0002-0613-6131"},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jason Cantarella","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030475064","display_name":"Meredith Perrie Casey","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meredith Perrie Casey","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047539877","display_name":"Eleanor Dannenberg","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eleanor Dannenberg","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021113224","display_name":"Whitney George","orcid":"https://orcid.org/0000-0001-8727-8483"},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Whitney George","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114022356","display_name":"Aja Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aja Johnson","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112469734","display_name":"A.C. Kelley","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amelia Kelley","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044269457","display_name":"Al LaPointe","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Al LaPointe","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023824306","display_name":"Matt Mastin","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matt Mastin","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057655210","display_name":"Jason Parsley","orcid":null},"institutions":[{"id":"https://openalex.org/I47251452","display_name":"Wake Forest University","ror":"https://ror.org/0207ad724","country_code":"US","type":"education","lineage":["https://openalex.org/I47251452"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jason Parsley","raw_affiliation_strings":["Wake Forest University, Mathematics Department, PO Box 7388, Winston-Salem, NC 27109, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wake Forest University, Mathematics Department, PO Box 7388, Winston-Salem, NC 27109, USA","institution_ids":["https://openalex.org/I47251452"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033679798","display_name":"Jacob Rooney","orcid":null},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacob Rooney","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000063587","display_name":"Rachel J. Whitaker","orcid":"https://orcid.org/0000-0003-2263-5798"},"institutions":[{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rachel Whitaker","raw_affiliation_strings":["University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Georgia, Mathematics Department, Boyd GSRC, Athens, GA 30602, USA","institution_ids":["https://openalex.org/I165733156"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081432563"],"corresponding_institution_ids":["https://openalex.org/I165733156"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.1829,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86517544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"1","first_page":"143","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9746000170707703,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/symmetry","display_name":"Symmetry (geometry)","score":0.6011180281639099},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4534963071346283},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4319967031478882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3476508855819702},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3353804349899292},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.32458215951919556},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2174256145954132}],"concepts":[{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6011180281639099},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4534963071346283},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4319967031478882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3476508855819702},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3353804349899292},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.32458215951919556},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2174256145954132}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym4010143","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym4010143","pdf_url":"https://www.mdpi.com/2073-8994/4/1/143/pdf?version=1329728487","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1010.3234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.3234","pdf_url":"https://arxiv.org/pdf/1010.3234","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:e318a84ac7684483b907c8c679f06787","is_oa":true,"landing_page_url":"https://doaj.org/article/e318a84ac7684483b907c8c679f06787","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 4, Iss 1, Pp 143-207 (2012)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/4/1/143/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym4010143","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 4; Issue 1; Pages: 143-207","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym4010143","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym4010143","pdf_url":"https://www.mdpi.com/2073-8994/4/1/143/pdf?version=1329728487","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2055393713.pdf","grobid_xml":"https://content.openalex.org/works/W2055393713.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W23023872","https://openalex.org/W135079182","https://openalex.org/W1495116500","https://openalex.org/W1561680070","https://openalex.org/W1983151696","https://openalex.org/W1985991462","https://openalex.org/W1986803408","https://openalex.org/W1998772422","https://openalex.org/W2017961228","https://openalex.org/W2031991375","https://openalex.org/W2071743839","https://openalex.org/W2124774360","https://openalex.org/W2142267869","https://openalex.org/W2231995711","https://openalex.org/W2339205572","https://openalex.org/W2493056632","https://openalex.org/W4234660042","https://openalex.org/W6703338536"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W4231291595","https://openalex.org/W4245609766","https://openalex.org/W1606211735","https://openalex.org/W2329192282","https://openalex.org/W2026588291"],"abstract_inverted_index":{"We":[0,17],"present":[1,48],"an":[2],"elementary":[3],"derivation":[4],"of":[5,12,34,37,44],"the":[6,31,35,38,52],"\u201cintrinsic\u201d":[7],"symmetry":[8,32,53],"groups":[9],"for":[10,40,55],"links":[11,46],"8":[13],"or":[14],"fewer":[15],"crossings.":[16],"show":[18],"that":[19],"standard":[20],"invariants":[21],"are":[22],"enough":[23],"to":[24],"rule":[25],"out":[26],"all":[27,41],"potential":[28],"symmetries":[29],"outside":[30],"group":[33,36,54],"link":[39],"but":[42],"one":[43],"these":[45],"and":[47],"explicit":[49],"isotopies":[50],"generating":[51],"every":[56],"link.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}