{"id":"https://openalex.org/W3048807427","doi":"https://doi.org/10.1090/mcom/3696","title":"Enumeration of set-theoretic solutions to the Yang\u2013Baxter equation","display_name":"Enumeration of set-theoretic solutions to the Yang\u2013Baxter equation","publication_year":2021,"publication_date":"2021-09-15","ids":{"openalex":"https://openalex.org/W3048807427","doi":"https://doi.org/10.1090/mcom/3696","mag":"3048807427"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3696","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3696","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.04483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067041446","display_name":"\u00d6zg\u00fcr Akg\u00fcn","orcid":"https://orcid.org/0000-0001-9519-938X"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"\u00d6. Akg\u00fcn","raw_affiliation_strings":["School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, United Kingdom","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014497246","display_name":"Mart\u0131\u0301n Mereb","orcid":null},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I24354313","display_name":"Universidad de Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"M. Mereb","raw_affiliation_strings":["IMAS\u00e2\u0080\u0093CONICET and Depto. de Matem\u00c3\u00a1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina","IMAS\u2013CONICET and Depto. de Matem\u00e1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMAS\u00e2\u0080\u0093CONICET and Depto. de Matem\u00c3\u00a1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina","institution_ids":["https://openalex.org/I24354313"]},{"raw_affiliation_string":"IMAS\u2013CONICET and Depto. de Matem\u00e1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina","institution_ids":["https://openalex.org/I24354313","https://openalex.org/I151201029"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061348450","display_name":"Leandro Vendramin","orcid":"https://orcid.org/0000-0003-0954-7785"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]},{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I24354313","display_name":"Universidad de Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]}],"countries":["AR","BE"],"is_corresponding":false,"raw_author_name":"L. Vendramin","raw_affiliation_strings":["IMAS\u00e2\u0080\u0093CONICET and Depto. de Matem\u00c3\u00a1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina; and Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium","IMAS\u2013CONICET and Depto. de Matem\u00e1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina","Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMAS\u00e2\u0080\u0093CONICET and Depto. de Matem\u00c3\u00a1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina; and Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium","institution_ids":["https://openalex.org/I13469542"]},{"raw_affiliation_string":"IMAS\u2013CONICET and Depto. de Matem\u00e1tica, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina","institution_ids":["https://openalex.org/I24354313","https://openalex.org/I151201029"]},{"raw_affiliation_string":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium","institution_ids":["https://openalex.org/I13469542"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067041446"],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":null,"apc_paid":null,"fwci":2.1198,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.88495144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"91","issue":"335","first_page":"1469","last_page":"1481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9973999857902527,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9966999888420105,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.996399998664856,"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/enumeration","display_name":"Enumeration","score":0.9035812616348267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8994579315185547},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6519577503204346},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6060925722122192},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5369012355804443},{"id":"https://openalex.org/keywords/yang\u2013baxter-equation","display_name":"Yang\u2013Baxter equation","score":0.5105160474777222},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4724576771259308},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3726755380630493},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3375836908817291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3056200444698334},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07601767778396606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04993113875389099},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.04904928803443909}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.9035812616348267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8994579315185547},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6519577503204346},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6060925722122192},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5369012355804443},{"id":"https://openalex.org/C177858542","wikidata":"https://www.wikidata.org/wiki/Q4476530","display_name":"Yang\u2013Baxter equation","level":3,"score":0.5105160474777222},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4724576771259308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3726755380630493},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3375836908817291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3056200444698334},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07601767778396606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04993113875389099},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.04904928803443909},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3696","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3696","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:vubissmart:VUBISSMART:2000:161009","is_oa":false,"landing_page_url":"https://biblio.vub.ac.be/vubir/enumeration-of-settheoretic-solutions-to-the-yangbaxter-equation(35f28e19-0403-45dc-a819-26b327a3759a).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:arXiv.org:2008.04483","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.04483","pdf_url":"https://arxiv.org/pdf/2008.04483","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":null,"raw_type":"text"},{"id":"pmh:oai:research-repository.st-andrews.ac.uk:10023/24851","is_oa":false,"landing_page_url":"https://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2022-03696-6/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"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":"Journal article"},{"id":"pmh:oai:vubissmart:VUBISSMART:2000:191208","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402573","display_name":"VUBIR (Vrije Universiteit Brussel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13469542","host_organization_name":"Vrije Universiteit Brussel","host_organization_lineage":["https://openalex.org/I13469542"],"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.04483","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.04483","pdf_url":"https://arxiv.org/pdf/2008.04483","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1235224426","display_name":null,"funder_award_id":"PICT 2018-3511","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G6637697873","display_name":null,"funder_award_id":"PICT 2018-3511","funder_id":"https://openalex.org/F4320334832","funder_display_name":"Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"}],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320334832","display_name":"Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/03stxzb56"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W35498873","https://openalex.org/W125104156","https://openalex.org/W245683260","https://openalex.org/W854777502","https://openalex.org/W1503971394","https://openalex.org/W1510365646","https://openalex.org/W1520688394","https://openalex.org/W1598380601","https://openalex.org/W1633336122","https://openalex.org/W1793020813","https://openalex.org/W1847403720","https://openalex.org/W1965612022","https://openalex.org/W1995969674","https://openalex.org/W2002863566","https://openalex.org/W2016030731","https://openalex.org/W2036224501","https://openalex.org/W2052372389","https://openalex.org/W2060042761","https://openalex.org/W2063107648","https://openalex.org/W2090149729","https://openalex.org/W2118905382","https://openalex.org/W2129464410","https://openalex.org/W2135745986","https://openalex.org/W2148550373","https://openalex.org/W2257802633","https://openalex.org/W2323563569","https://openalex.org/W2424997766","https://openalex.org/W2610839977","https://openalex.org/W2625398403","https://openalex.org/W2732254484","https://openalex.org/W2734924814","https://openalex.org/W2898780680","https://openalex.org/W2900770265","https://openalex.org/W2903296472","https://openalex.org/W2935937670","https://openalex.org/W2937456597","https://openalex.org/W2941999232","https://openalex.org/W2953180333","https://openalex.org/W2962756223","https://openalex.org/W2962878588","https://openalex.org/W2963045431","https://openalex.org/W2963154383","https://openalex.org/W2963189412","https://openalex.org/W2963289915","https://openalex.org/W2963359858","https://openalex.org/W2963518811","https://openalex.org/W2963766270","https://openalex.org/W2964137740","https://openalex.org/W3001574459","https://openalex.org/W3100083134","https://openalex.org/W3101270604","https://openalex.org/W3104248411","https://openalex.org/W3106207486","https://openalex.org/W4231555203","https://openalex.org/W6631133807","https://openalex.org/W6640852056","https://openalex.org/W6761158915"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W2406961474","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2952598754","https://openalex.org/W3042106073","https://openalex.org/W2143566611","https://openalex.org/W588267724","https://openalex.org/W2949852903","https://openalex.org/W4298540939"],"abstract_inverted_index":{"We":[0,18],"use":[1],"Constraint":[2],"Satisfaction":[3],"methods":[4],"to":[5,11,47],"enumerate":[6,48],"and":[7,35],"construct":[8],"set-theoretic":[9],"solutions":[10,25,31],"the":[12],"Yang\u2013Baxter":[13],"equation":[14],"of":[15,26,32,39],"small":[16],"size.":[17],"show":[19],"that":[20],"there":[21],"are":[22],"321,931":[23],"involutive":[24,30],"size":[27,33,40],"nine,":[28],"4,895,272":[29],"ten":[34],"422,449,480":[36],"non-involutive":[37,49],"solution":[38],"eight.":[41],"Our":[42],"method":[43],"is":[44],"then":[45],"used":[46],"biquandles.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}
