Document Zbl 07963365

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Knot Theory Ramifications</a> <a href="/?q=in%3A522112" title="Articles in this Issue">33, No. 14, Article ID 2450052, 15 p. (2024)</a>. </div> <div class="abstract">Summary: We present the $CWR$ invariant, a new invariant for alternating links, which builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an array of two-variable polynomials that provides a stronger invariant compared to the $WRP$ invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman 3-variable, and Kauffman 2-variable polynomials on specific knot examples. Additionally, we derive general recursive “skein” relations, and also specific formulas for the initial components of the $CWR$ invariant using weighted adjacency matrices of modified Tait graphs.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A57K10" title="MSC2020">57K10</a> </td> <td class="space"> Knot theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A57K14" title="MSC2020">57K14</a> </td> <td class="space"> Knot polynomials </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aknot+invariant">knot invariant</a>; <a href="/?q=ut%3Alink+invariant">link invariant</a>; <a href="/?q=ut%3Aalternating+knot">alternating knot</a>; <a href="/?q=ut%3ACWR+invariant">CWR invariant</a>; <a href="/?q=ut%3Aknots+tabulation">knots tabulation</a></div> <div class="software"> <h3>Software:</h3><a href="/software/825">SageMath</a>; <a href="/software/6874">SnapPy</a>; <a href="/software/12471">KnotInfo</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07963365" data-ciurl="/ci/07963365" data-biburl="/bibtex/07963365.bib" data-amsurl="/amsrefs/07963365.bib" data-xmlurl="/xml/07963365.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07963365.pdf" title="Zbl 07963365 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1142/S0218216524500524" aria-label="DOI for “CWR sequence of invariants of alternating links and its properties”" title="10.1142/S0218216524500524">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2406.04987"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">D. 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Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds, http://snappy.computop.org.</td> </tr><tr> <td>[5]</td> <td class="space">Developers, The Sage, Sagemath, the Sage Mathematics Software System (Version 10.1), (2023), https://www.sagemath.org.</td> </tr><tr> <td>[6]</td> <td class="space">Freyd, P., Yetter, D., Hoste, J., Lickorish, W. B. R., Millett, K. and Ocneanu, A., A new polynomial invariant of knots and links, Bull. Amer. Math. Soc.12 (1985) 239-246. · <a href="/0572.57002" class="nowrap">Zbl 0572.57002</a></td> </tr><tr> <td>[7]</td> <td class="space">Jabłonowski, M., A polynomial pair invariant of alternating knots and links, J. Knot Theory Ramifications, https://doi.org/10.1142/S0218216524500482 · <a href="/07963363" class="nowrap">Zbl 07963363</a></td> </tr><tr> <td>[8]</td> <td class="space">Kauffman, L. H., New invariants in the theory of knots, Amer. Math. Mon.95 (1988) 195-242. · <a href="/0657.57001" class="nowrap">Zbl 0657.57001</a></td> </tr><tr> <td>[9]</td> <td class="space">Kauffman, L. H., A Tutte polynomial for signed graphs, Discr. Appl. Math.25 (1989) 105-127. · <a href="/0698.05026" class="nowrap">Zbl 0698.05026</a></td> </tr><tr> <td>[10]</td> <td class="space">Kauffman, L. H., An invariant of regular isotopy, Trans. Amer. Math. Soc.318 (1990) 417-471. · <a href="/0763.57004" class="nowrap">Zbl 0763.57004</a></td> </tr><tr> <td>[11]</td> <td class="space">Knauer, U. and Knauer, K., Algebraic Graph Theory: Morphisms, Monoids and Matrices, , Vol. 41 (Walter de Gruyter GmbH, 2019). · <a href="/1425.05003" class="nowrap">Zbl 1425.05003</a></td> </tr><tr> <td>[12]</td> <td class="space">Lafferty, K., The three-variable bracket polynomial for reduced, alternating links, Rose-Hulman Undergraduate Math. J.14 (2013) 98-113. · <a href="/1398.57018" class="nowrap">Zbl 1398.57018</a></td> </tr><tr> <td>[13]</td> <td class="space">Listing, J. B., Vorstudien zur Topologie, Gottinger Studien (Abtheilung 1)1 (1847) 811-875.</td> </tr><tr> <td>[14]</td> <td class="space">C. Livingston and A. H. Moore, KnotInfo: Table of Knot Invariants, https://knotinfo.math.indiana.edu/.</td> </tr><tr> <td>[15]</td> <td class="space">Menasco, W., Alternating knots, in Encyclopedia Knot Theory (CRC Press, 2021), pp. 167-178. · <a href="/1465.57063" class="nowrap">Zbl 1465.57063</a></td> </tr><tr> <td>[16]</td> <td class="space">Menasco, W. and Thistlethwaite, M. B., The Tait flyping conjecture, Bull. Amer. Math. Soc.25 (1991) 403-412. · <a href="/0745.57002" class="nowrap">Zbl 0745.57002</a></td> </tr><tr> <td>[17]</td> <td class="space">Menasco, W. and Thistlethwaite, M. B., The classification of alternating links, Ann. 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B., Kauffman’s polynomial and alternating links, Topology27 (1988) 311-318. · <a href="/0667.57002" class="nowrap">Zbl 0667.57002</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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