{"id":"https://openalex.org/W7204932191","doi":"https://doi.org/10.48550/arxiv.2608.30132","title":"R-equivalence of quandle colorings and inner automorphisms","display_name":"R-equivalence of quandle colorings and inner automorphisms","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204932191","doi":"https://doi.org/10.48550/arxiv.2608.30132"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30132","pdf_url":"https://arxiv.org/pdf/2608.30132","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30132","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129032194","display_name":"Mai Sato","orcid":"https://orcid.org/0009-0003-5610-5709","observed_orcids":["https://orcid.org/0009-0003-5610-5709"]},"institutions":[{"id":"https://openalex.org/I183594015","display_name":"Tsuda University","ror":"https://ror.org/027mg2511","country_code":"JP","type":"education","lineage":["https://openalex.org/I183594015"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Sato, Mai","raw_affiliation_strings":["Department of Mathematics , Tsuda University , 2-1-1 Tsuda-machi , Kodaira-shi , Tokyo 187-8577 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Tsuda University , 2-1-1 Tsuda-machi , Kodaira-shi , Tokyo 187-8577 , Japan","institution_ids":["https://openalex.org/I183594015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5129032194"],"corresponding_institution_ids":["https://openalex.org/I183594015"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9965999722480774,"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":0.9965999722480774,"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/T12504","display_name":"Mathematics and Applications","score":0.00039999998989515007,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/r-equivalence","display_name":"R-equivalence","score":0.8640000224113464},{"id":"https://openalex.org/keywords/inner-automorphism-group","display_name":"inner automorphism group","score":0.824999988079071},{"id":"https://openalex.org/keywords/knot-diagrams","display_name":"knot diagrams","score":0.718999981880188},{"id":"https://openalex.org/keywords/two-bridge-knots","display_name":"2-bridge knots","score":0.9350000023841858},{"id":"https://openalex.org/keywords/knot-invariants","display_name":"knot invariants","score":0.8080000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8450999855995178},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.7803999781608582},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5392000079154968},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.474700003862381},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3100000023841858},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.28630000352859497},{"id":"https://openalex.org/C133776654","wikidata":"https://www.wikidata.org/wiki/Q2381352","display_name":"Fibered knot","level":2,"score":0.26179999113082886}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30132","pdf_url":"https://arxiv.org/pdf/2608.30132","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,"listed_in":[],"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":"doi:10.48550/arxiv.2608.30132","doi":"https://doi.org/10.48550/arxiv.2608.30132","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30132","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30132","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30132","pdf_url":"https://arxiv.org/pdf/2608.30132","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204932191.pdf","grobid_xml":"https://content.openalex.org/works/W7204932191.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1575525560"],"related_works":["https://openalex.org/W7135195355","https://openalex.org/W6910628777","https://openalex.org/W7202124123","https://openalex.org/W4399567703","https://openalex.org/W3100774870","https://openalex.org/W3131191500","https://openalex.org/W4226163799","https://openalex.org/W64663503","https://openalex.org/W4410040531","https://openalex.org/W3206110182"],"abstract_inverted_index":{"R-equivalence":[0,38,51],"is":[1],"an":[2,11],"equivalence":[3],"relation":[4],"on":[5,36],"the":[6,28,37,45,50],"set":[7],"of":[8,10,27,32,40,53,55,58],"colorings":[9,54],"oriented":[12],"knot":[13,61],"diagram":[14,57],"by":[15,44,62],"a":[16,24,33,41,56,59,63,68],"quandle.":[17,46],"In":[18],"this":[19],"paper,":[20],"we":[21],"show":[22],"that":[23],"certain":[25,69],"subgroup":[26],"inner":[29],"automorphism":[30],"group":[31],"quandle":[34,65],"acts":[35],"class":[39],"given":[42],"coloring":[43],"We":[47],"also":[48],"determine":[49],"classes":[52],"$2$-bridge":[60],"dihedral":[64],"completely,":[66],"under":[67],"condition.":[70]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
