{"id":"https://openalex.org/W1566601065","doi":"https://doi.org/10.4169/amer.math.monthly.124.1.4","title":"Neighbors of Knots in the Gordian Graph","display_name":"Neighbors of Knots in the Gordian Graph","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W1566601065","doi":"https://doi.org/10.4169/amer.math.monthly.124.1.4","mag":"1566601065"},"language":"en","primary_location":{"id":"doi:10.4169/amer.math.monthly.124.1.4","is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.124.1.4","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1505.00201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073716471","display_name":"Ryan Blair","orcid":"https://orcid.org/0000-0002-2547-8874"},"institutions":[{"id":"https://openalex.org/I59897056","display_name":"California State University, Long Beach","ror":"https://ror.org/0080fxk18","country_code":"US","type":"education","lineage":["https://openalex.org/I59897056"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ryan Blair","raw_affiliation_strings":["California State University, Long Beach Long Beach, CA 90840 ryan.blair@csulb.edu"],"affiliations":[{"raw_affiliation_string":"California State University, Long Beach Long Beach, CA 90840 ryan.blair@csulb.edu","institution_ids":["https://openalex.org/I59897056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081180065","display_name":"Marion Campisi","orcid":"https://orcid.org/0000-0002-5735-3099"},"institutions":[{"id":"https://openalex.org/I2801551205","display_name":"The Ohio State University at Marion","ror":"https://ror.org/03646q924","country_code":"US","type":"education","lineage":["https://openalex.org/I2801551205","https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marion Campisi","raw_affiliation_strings":["marion.campisi@sjsu.edu"],"affiliations":[{"raw_affiliation_string":"marion.campisi@sjsu.edu","institution_ids":["https://openalex.org/I2801551205"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112447144","display_name":"Jesse Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I9553001","display_name":"Mathys (Netherlands)","ror":"https://ror.org/00vj56071","country_code":"NL","type":"company","lineage":["https://openalex.org/I9553001"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jesse Johnson","raw_affiliation_strings":["jejo.math@gmail.com"],"affiliations":[{"raw_affiliation_string":"jejo.math@gmail.com","institution_ids":["https://openalex.org/I9553001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078189551","display_name":"Scott A. Taylor","orcid":"https://orcid.org/0000-0001-9580-9125"},"institutions":[{"id":"https://openalex.org/I27504731","display_name":"Colby College","ror":"https://ror.org/00fvyjk73","country_code":"US","type":"education","lineage":["https://openalex.org/I27504731"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott A. Taylor","raw_affiliation_strings":["Colby College, Waterville, ME 04901 scott.taylor@colby.edu"],"affiliations":[{"raw_affiliation_string":"Colby College, Waterville, ME 04901 scott.taylor@colby.edu","institution_ids":["https://openalex.org/I27504731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033054843","display_name":"Maggy Tomova","orcid":null},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maggy Tomova","raw_affiliation_strings":["The University of Iowa, Iowa City, IA 52240 maggy-tomova@uiowa.edu"],"affiliations":[{"raw_affiliation_string":"The University of Iowa, Iowa City, IA 52240 maggy-tomova@uiowa.edu","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5073716471"],"corresponding_institution_ids":["https://openalex.org/I59897056"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0066547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"124","issue":"1","first_page":"4","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.960099995136261,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9440000057220459,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.524435818195343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4362868666648865},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4293590486049652},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3466182053089142}],"concepts":[{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.524435818195343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4362868666648865},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4293590486049652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3466182053089142}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.4169/amer.math.monthly.124.1.4","is_oa":false,"landing_page_url":"https://doi.org/10.4169/amer.math.monthly.124.1.4","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1505.00201","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.00201","pdf_url":"https://arxiv.org/pdf/1505.00201","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:1566601065","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1505.00201.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1505.00201","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1505.00201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1505.00201","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.00201","pdf_url":"https://arxiv.org/pdf/1505.00201","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W80134341","https://openalex.org/W580052950","https://openalex.org/W1483883278","https://openalex.org/W1619157788","https://openalex.org/W1969319101","https://openalex.org/W1981331759","https://openalex.org/W1984133736","https://openalex.org/W1984199069","https://openalex.org/W2012346366","https://openalex.org/W2020547005","https://openalex.org/W2028806726","https://openalex.org/W2039040964","https://openalex.org/W2060710910","https://openalex.org/W2105917837","https://openalex.org/W2119010810","https://openalex.org/W2146469364","https://openalex.org/W2888943156"],"related_works":["https://openalex.org/W2963359370","https://openalex.org/W1571480860","https://openalex.org/W1831875708","https://openalex.org/W2077488685","https://openalex.org/W1988239252","https://openalex.org/W3041611782","https://openalex.org/W2951797369","https://openalex.org/W2346074715","https://openalex.org/W2016313155","https://openalex.org/W1760969156","https://openalex.org/W2612661780","https://openalex.org/W2091804597","https://openalex.org/W2435985484","https://openalex.org/W1991274038","https://openalex.org/W3103455635","https://openalex.org/W1723973337","https://openalex.org/W2740178932","https://openalex.org/W2128758915","https://openalex.org/W2280429843","https://openalex.org/W2075646361"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"every":[3],"knot":[4,12],"is":[5],"one":[6],"crossing":[7],"change":[8],"away":[9],"from":[10],"a":[11],"of":[13],"arbitrarily":[14,19],"high":[15,20],"bridge":[16,21],"number":[17],"and":[18],"distance.":[22]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
