{"title":"Describing Realizable Gauss Diagrams Using the Concepts of Parity or Bipartite Graphs","authors":"A. Lisitsa, V. Lopatkin, A. Vernitski","doi":"10.1142/s0218216523500591","DOIUrl":"https://doi.org/10.1142/s0218216523500591","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41942795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Topological Quandles up to four Elements","authors":"M. Ayadi","doi":"10.1142/s0218216523500967","DOIUrl":"https://doi.org/10.1142/s0218216523500967","url":null,"abstract":"The finite topological quandles can be represented as $ntimes n$ matrices, recently defined by S. Nelson and C. Wong. In this paper, we first study the finite topological quandles and we show how to use these matrices to distinguish all isomorphism classes of finite topological quandles for a given cardinality $n$. As an application, we classify finite topological quandles with up to 4 elements.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"78 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139361145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Torus knots and links in V1 that are invariant under the ℤm × ℤl-actions on V1 that form the quotient orbifold (A0,k","authors":"Aruna Bandara","doi":"10.1142/s0218216523500542","DOIUrl":"https://doi.org/10.1142/s0218216523500542","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44014681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A polynomial invariant of Kauffman type for knotoids","authors":"Y. Miyazawa","doi":"10.1142/s0218216523500505","DOIUrl":"https://doi.org/10.1142/s0218216523500505","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47127027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A polyhedral approach to the arithmetic and geometry of hyperbolic link complements","authors":"R. Kellerhals","doi":"10.1142/s0218216523500529","DOIUrl":"https://doi.org/10.1142/s0218216523500529","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43763894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"In Memory of Vaughan Jones (Renzo L. Ricca)","authors":"","doi":"10.1142/s0218216523400254","DOIUrl":"https://doi.org/10.1142/s0218216523400254","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43669610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Cheong, Alexander Doser, McKinley Gray, S. Sawin
{"title":"Relationship of the Hennings and Witten-Reshetikhan-Turaev Invariants for Higher Rank Quantum Groups","authors":"W. Cheong, Alexander Doser, McKinley Gray, S. Sawin","doi":"10.1142/s0218216523500487","DOIUrl":"https://doi.org/10.1142/s0218216523500487","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45730029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial","authors":"Butian Zhang","doi":"10.1142/s0218216523500840","DOIUrl":"https://doi.org/10.1142/s0218216523500840","url":null,"abstract":"A state model for Kauffman polynomial of Dubrovnik-version is given. Based on the state model, the Gauss diagram formulae for Vassiliev invariants are given from the coefficients of Kauffman polynomial following the method of Chmutov and Polyak. Some arrow diagram identities are given to simplify the Gauss diagram formulae of order 3, which give Polyak-Viro and Chmutov-Polyak formulae for the Vassiliev invariant of order 3. The models of Kauffman polynomial and HOMFLY-PT polynomial give different Gauss diagram expressions when specializing to Jones poynomial.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139371070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on Rivin's interpretation of McShane's identity as identities for closed geodesics with one self-intersection","authors":"D. Lei, Ying Zhang","doi":"10.1142/s0218216523500499","DOIUrl":"https://doi.org/10.1142/s0218216523500499","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41455492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Homotopy classes of 4-component links, claspers and the habegger-lin algorithm","authors":"Yuka Kotorii, Atsuhiko Mizusawa","doi":"10.1142/s0218216523500451","DOIUrl":"https://doi.org/10.1142/s0218216523500451","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49480903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}