DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jeong, Myeong-Ju | ko |
dc.contributor.author | Park, Chan-Young | ko |
dc.date.accessioned | 2015-03-27T08:06:32Z | - |
dc.date.available | 2015-03-27T08:06:32Z | - |
dc.date.created | 2014-11-11 | - |
dc.date.created | 2014-11-11 | - |
dc.date.issued | 2014-06 | - |
dc.identifier.citation | JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.23, no.7 | - |
dc.identifier.issn | 0218-2165 | - |
dc.identifier.uri | http://hdl.handle.net/10203/194548 | - |
dc.description.abstract | Y. Miyazawa introduced a two-variable polynomial invariant of virtual knots in 2006 [Magnetic graphs and an invariant for virtual links, J. Knot Theory Ramifications 15 (2006) 1319-1334] and then generalized it to give a multi-variable one via decorated virtual magnetic graph diagrams in 2008. A. Ishii gave a simple state model for the two-variable Miyazawa polynomial by using pole diagrams in 2008 [A multi-variable polynomial invariant for virtual knots and links, J. Knot Theory Ramifications 17 (2008) 1311-1326]. H. A. Dye and L. H. Kauffman constructed an arrow polynomial of a virtual link in 2009 which is equivalent to the multi-variable Miyazawa polynomial [Virtual crossing number and the arrow polynomial, preprint (2008), arXiv: 0810.3858v3, http://front.math.ucdavis.edu.]. We give a bracket model for the multi-variable Miyazawa polynomial via pole diagrams and polar tangles similarly to the Ishii's state model for the two-variable polynomial. By normalizing the bracket polynomial we get the multi-variable Miyazawa polynomial f(K) is an element of Z[A, A(-1), K-1, K-2,...] of a virtual link K. n-similar knots take the same value for any Vassiliev invariant of degree < n. We show that f(K1) = f(K2) mod (A(4) -1)(n) if two virtual links K-1 and K-2 are n-similar. Also we give a necessary condition for a virtual link to be periodic by using n-similarity of virtual tangles and the Miyazawa polynomial. | - |
dc.language | English | - |
dc.publisher | WORLD SCIENTIFIC PUBL CO PTE LTD | - |
dc.subject | FINITE-TYPE INVARIANTS | - |
dc.subject | VASSILIEV INVARIANTS | - |
dc.subject | KNOTS | - |
dc.title | Similarity indices and the Miyazawa polynomials of virtual links | - |
dc.type | Article | - |
dc.identifier.wosid | 000342987500004 | - |
dc.identifier.scopusid | 2-s2.0-84928372499 | - |
dc.type.rims | ART | - |
dc.citation.volume | 23 | - |
dc.citation.issue | 7 | - |
dc.citation.publicationname | JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | - |
dc.identifier.doi | 10.1142/S0218216514600037 | - |
dc.contributor.nonIdAuthor | Park, Chan-Young | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Virtual link | - |
dc.subject.keywordAuthor | multi-variable Miyazawa polynomial | - |
dc.subject.keywordAuthor | polar link | - |
dc.subject.keywordAuthor | similarity index | - |
dc.subject.keywordPlus | FINITE-TYPE INVARIANTS | - |
dc.subject.keywordPlus | VASSILIEV INVARIANTS | - |
dc.subject.keywordPlus | KNOTS | - |
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