Relevant bibliographies by topics / Knot polynomials

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Knot polynomials'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Knot polynomials"

1

Takioka, Hideo. "Infinitely many knots with the trivial (2,1)-cable Γ-polynomial". Journal of Knot Theory and Its Ramifications 27, № 02 (2018): 1850013. http://dx.doi.org/10.1142/s021821651850013x.

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For coprime integers [Formula: see text] and [Formula: see text], the [Formula: see text]-cable [Formula: see text]-polynomial of a knot is the [Formula: see text]-polynomial of the [Formula: see text]-cable knot of the knot, where the [Formula: see text]-polynomial is the common zeroth coefficient polynomial of the HOMFLYPT and Kauffman polynomials. In this paper, we show that there exist infinitely many knots with the trivial [Formula: see text]-cable [Formula: see text]-polynomial, that is, the [Formula: see text]-cable [Formula: see text]-polynomial of the trivial knot. Moreover, we see th
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2

Mellor, Blake. "Alexander and writhe polynomials for virtual knots." Journal of Knot Theory and Its Ramifications 25, no. 08 (2016): 1650050. http://dx.doi.org/10.1142/s0218216516500504.

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We give a new interpretation of the Alexander polynomial [Formula: see text] for virtual knots due to Sawollek [On Alexander–Conway polynomials for virtual knots and Links, preprint (2001), arXiv:math/9912173] and Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications 12 (2003) 987–1000], and use it to show that, for any virtual knot, [Formula: see text] determines the writhe polynomial of Cheng and Gao [A polynomial invariant of virtual links, J. Knot Theory Ramifications 22(12) (2013), Article ID: 1341002, 33pp.] (equivalently, Kauffman’s affine index polyn
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JEONG, MYEONG-JU, and CHAN-YOUNG PARK. "LENS KNOTS, PERIODIC LINKS AND VASSILIEV INVARIANTS." Journal of Knot Theory and Its Ramifications 13, no. 08 (2004): 1041–56. http://dx.doi.org/10.1142/s0218216504003615.

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In this paper, we study lens knots and periodic knots by using integral Vassiliev invariants. Knot polynomials such as the Jones, HOMFLY, Kauffman polynomials give infinitely many integral Vassiliev invariants and we get some necessary conditions for a link to be a lens knot or a periodic link by using these polynomial invariants.
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Nguyen, Hoang-An, and Anh T. Tran. "Adjoint twisted Alexander polynomial of twisted Whitehead links." Journal of Knot Theory and Its Ramifications 27, no. 04 (2018): 1850026. http://dx.doi.org/10.1142/s0218216518500268.

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The adjoint twisted Alexander polynomial has been computed for twist knots [A. Tran, Twisted Alexander polynomials with the adjoint action for some classes of knots, J. Knot Theory Ramifications 23(10) (2014) 1450051], genus one two-bridge knots [A. Tran, Adjoint twisted Alexander polynomials of genus one two-bridge knots, J. Knot Theory Ramifications 25(10) (2016) 1650065] and the Whitehead link [J. Dubois and Y. Yamaguchi, Twisted Alexander invariant and nonabelian Reidemeister torsion for hyperbolic three dimensional manifolds with cusps, Preprint (2009), arXiv:0906.1500 ]. In this paper, w
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Guevara Hernández, María de los Angeles, and Hugo Cabrera Ibarra. "Infinite families of prime knots with alt(K) = 1 and their Alexander polynomials." Journal of Knot Theory and Its Ramifications 28, no. 02 (2019): 1950010. http://dx.doi.org/10.1142/s021821651950010x.

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In this paper, we construct, by using the Alexander polynomial, infinite families of nonalternating prime knots, which have alternation number equal to one. More specifically these knots after one crossing change yield a 2-bridge knot or the trivial knot. In particular, we display two infinite families of nonalternating knots and their Alexander polynomials. Moreover, we give formulae to obtain the Conway and Alexander polynomials of oriented 3-tangles and the links formed from their closure with a specific orientation. In particular, we propose a construction to form families of links for whi
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Stoimenow, A. "On Cabled Knots and Vassiliev Invariants (Not) Contained in Knot Polynomials." Canadian Journal of Mathematics 59, no. 2 (2007): 418–48. http://dx.doi.org/10.4153/cjm-2007-018-0.

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AbstractIt is known that the Brandt–Lickorish–Millett–Ho polynomial Q contains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable from Q is an open problem. We show that this is not so up to degree 9. We also give the (apparently) first examples of knots not distinguished by 2-cable HOMFLY polynomials which are not mutants. Our calculations provide evidence of a negative answer to the question whether Vassiliev knot invariants of degree d ≤ 10 are determined by the HOMFLY and Kauffman polynomials and their 2-cables, and for the existence of alge
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Berest, Yuri, and Peter Samuelson. "Double affine Hecke algebras and generalized Jones polynomials." Compositio Mathematica 152, no. 7 (2016): 1333–84. http://dx.doi.org/10.1112/s0010437x16007314.

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In this paper we propose and discuss implications of a general conjecture that there is a natural action of a rank 1 double affine Hecke algebra on the Kauffman bracket skein module of the complement of a knot $K\subset S^{3}$. We prove this in a number of nontrivial cases, including all $(2,2p+1)$ torus knots, the figure eight knot, and all 2-bridge knots (when $q=\pm 1$). As the main application of the conjecture, we construct three-variable polynomial knot invariants that specialize to the classical colored Jones polynomials introduced by Reshetikhin and Turaev. We also deduce some new prop
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KIM, TAEHEE, TAKAHIRO KITAYAMA, and TAKAYUKI MORIFUJI. "TWISTED ALEXANDER POLYNOMIALS ON CURVES IN CHARACTER VARIETIES OF KNOT GROUPS." International Journal of Mathematics 24, no. 03 (2013): 1350022. http://dx.doi.org/10.1142/s0129167x13500225.

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For a fibered knot in the 3-sphere the twisted Alexander polynomial associated to an SL(2, ℂ)-character is known to be monic. It is conjectured that for a nonfibered knot there is a curve component of the SL(2, ℂ)-character variety containing only finitely many characters whose twisted Alexander polynomials are monic, i.e. finiteness of such characters detects fiberedness of knots. In this paper, we discuss the existence of a certain curve component which relates to the conjecture when knots have nonmonic Alexander polynomials. We also discuss the similar problem of detecting the knot genus.
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LU, BIN, and JIANYUAN K. ZHONG. "THE KAUFFMAN POLYNOMIALS OF PRETZEL KNOTS." Journal of Knot Theory and Its Ramifications 17, no. 02 (2008): 157–69. http://dx.doi.org/10.1142/s0218216508006026.

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Let ℚ(α, s) be the field of rational functions in α, s. We compute the Kauffman polynomials of pretzel knots [1,6] using the Kauffman skein theory and linear algebra tools. We give a formula for the Kauffman polynomial of a pretzel knot such that after inputting the sequence notation of the pretzel knot, the output is its Kauffman polynomial. Our calculation can be implemented in Mathematica, Maple, Mathcad, etc.
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Takioka, Hideo. "A characterization of the Γ-polynomials of knots with clasp number at most two". Journal of Knot Theory and Its Ramifications 26, № 04 (2017): 1750013. http://dx.doi.org/10.1142/s0218216517500134.

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It is known that every knot bounds a singular disk with only clasp singularities, which is called a clasp disk. The clasp number of a knot is the minimum number of clasp singularities among all clasp disks of the knot. It is known that the Conway polynomials of knots with clasp number at most two are characterized. In this paper, we focus on the common zeroth coefficient polynomial of both the HOMFLYPT and Kauffman polynomials, which is called the [Formula: see text]-polynomial. As a result, we characterize the [Formula: see text]-polynomials of knots with clasp number at most two. Moreover, i
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Dissertations / Theses on the topic "Knot polynomials"

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Woodard, Mary Kay. "Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc501096/.

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The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define the Conway polynomial, the Axioms for Computation are given and many examples of their use are includ
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Sacdalan, Alvin Mendoza. "Aspects of the Jones polynomial." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/2872.

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A knot invariant called the Jones polynomial will be defined in two ways, as the Kauffman Bracket polynomial and the Tutte polynomial. Three properties of the Jones polynomial are discussed. We also see how mutant knots share the same Jones polynomial.
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Keever, Robert Dudley. "Some problems in knot theory." Thesis, University of Edinburgh, 1989. http://hdl.handle.net/1842/12219.

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Noble, Steven D. "The complexity of graph polynomials." Thesis, University of Oxford, 1997. http://ora.ox.ac.uk/objects/uuid:c84702b4-b371-474b-a003-4d24f25e5a12.

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This thesis examines graph polynomials and particularly their complexity. We give short proofs of two results from Gessel and Sagan (1996) which present new evaluations of the Tutte polynomial concerning orientations. A theorem of Massey et al (1997) gives an expression concerning the average size of a forest in a graph. We generalise this result to any simplicial complex. We answer a question posed by Kleinschmidt and Onn (1995) by showing that the language of partitionable simplicial complexes is in NP. We prove the following result concerning the complexity of the Tutte polynomial: Theorem
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Roberts, Sharleen Adrienne. "Knots Not for Naught." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1446.pdf.

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Jacobsson, Magnus. "Khovanov homology and link cobordisms /." Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3765.

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Lorton, Cody. "On the Breadth of the Jones Polynomial for Certain Classes of Knots and Links." TopSCHOLAR®, 2009. http://digitalcommons.wku.edu/theses/86.

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The problem of finding the crossing number of an arbitrary knot or link is a hard problem in general. Only for very special classes of knots and links can we solve this problem. Often we can only hope to find a lower bound on the crossing number Cr(K) of a knot or a link K by computing the Jones polynomial of K, V(K). The crossing number Cr(K) is bounded from below by the difference between the greatest degree and the smallest degree of the polynomial V(K). However the computation of the Jones polynomial of an arbitrary knot or link is also difficult in general. The goal of this thesis is to f
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Petersen, David Alan. "Tutte polynomial in knot theory." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3128.

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This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.
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Ameur, Kheira. "Polynomial quandle cocycles, their knot invariants and applications." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001813.

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Yokota, Yoshiyuki. "Polynomial invariants of periodic knots /." Electronic version of summary, 1992. http://www.wul.waseda.ac.jp/gakui/gaiyo/1852.pdf.

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Thesis (Sci. D.)--Waseda University, 1992.<br>Accompanied by summary (5 p. : ill. ; 26 cm.) in Japanese. Includes bibliographical references (leaves 58-59). "A list of papers by Yoshiyuki Yokota": leaf 60.
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Books on the topic "Knot polynomials"

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1945-, Kauffman Louis H., ed. Knots and applications. World Scientific, 1995.

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Ohtsuki, Tomotada. On the 2-loop polynomial of knots. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2005.

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Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. American Mathematical Society, 2015.

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Knots and Physics. World Scientific Publishing Co Pte Ltd, 2012.

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Knots and physics. 2nd ed. World Scientific, 1993.

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Knots and physics. 3rd ed. World Scientific, 2001.

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Knots and Physics. World Scientific Publishing Company, 2012.

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Knots and physics. World Scientific, 1991.

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Knots and Physics. World Scientific Publishing Co Pte Ltd, 2012.

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Knots and Physics. World Scientific Publishing Co Pte Ltd, 1994.

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Book chapters on the topic "Knot polynomials"

1

Kawauchi, Akio. "Multi-variable Alexander polynomials." In A Survey of Knot Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9227-8_8.

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Lickorish, W. B. Raymond. "Exploring the HOMFLY and Kauffman Polynomials." In An Introduction to Knot Theory. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0691-0_16.

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Harpe, P. "Introduction to Knot and Link Polynomials." In Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3005-6_17.

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Kawauchi, Akio. "Jones type polynomials II: an algebraic approach." In A Survey of Knot Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9227-8_10.

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Kawauchi, Akio. "Jones type polynomials I: a topological approach." In A Survey of Knot Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9227-8_9.

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Wu, Yong-Shi. "Topological Chern-Simons Gauge Theory and “New” Knot/Link Polynomials." In Differential Geometric Methods in Theoretical Physics. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-9148-7_55.

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Ricca, Renzo L. "Structural Complexity of Vortex Flows by Diagram Analysis and Knot Polynomials." In How Nature Works. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00254-5_5.

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Haglund, Jim. "The combinatorics of knot invariants arising from the study of Macdonald polynomials." In Recent Trends in Combinatorics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24298-9_23.

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Millett, Kenneth C. "Knot Theory, Jones’ Polynomials, Invariants of 3-Manifolds, and the Topological Theory of Fluid Dynamics." In Topological Aspects of the Dynamics of Fluids and Plasmas. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-017-3550-6_2.

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Przytycki, Józef H., Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega, and Deborah Weeks. "The Jones Polynomial and Kauffman Bracket Polynomial." In Lectures in Knot Theory. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-40044-5_5.

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Conference papers on the topic "Knot polynomials"

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Zhou, Tommy, Zhehan Wang, Atinderpal Singh Lakhan, Iyad Isleem, Mohammed Abuibaid, and Jun Steed Huang. "Multivariate Polynomial Public Key Digital Signature Trefoil Knot Algorithm." In 2024 13th International Conference on Communications, Circuits and Systems (ICCCAS). IEEE, 2024. http://dx.doi.org/10.1109/icccas62034.2024.10652771.

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LI, Xinfei, X. LIU, and Yong-chang Huang. "Tackling cosmic strings by knot polynomials." In Proceedings of the MG15 Meeting on General Relativity. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811258251_0161.

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Ricca, Renzo L. "Tackling fluid tangles complexity by knot polynomials." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756217.

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KANENOBU, TAIZO. "AN EVALUATION OF THE COEFFICIENT POLYNOMIALS OF THE HOMFLY POLYNOMIAL OF A LINK." In Proceedings of the International Conference on Knot Theory and Its Ramifications. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792679_0010.

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Mironov, A., and A. Morozov. "Equations on knot polynomials and 3d/5d duality." In THE SIXTH INTERNATIONAL SCHOOL ON FIELD THEORY AND GRAVITATION-2012. AIP, 2012. http://dx.doi.org/10.1063/1.4756970.

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Mironov, A., A. Morozov, and And Morozov. "Evolution method and “differential hierarchy” of colored knot polynomials." In NONLINEAR AND MODERN MATHEMATICAL PHYSICS: Proceedings of the 2nd International Workshop. AIP, 2013. http://dx.doi.org/10.1063/1.4828688.

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KAWAGOE, Kenichi. "LIMITS OF THE HOMFLY POLYNOMIALS OF THE FIGURE-EIGHT KNOT." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0018.

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Yamashita, Hiroki, and Hiroyuki Sugiyama. "Comparison of Finite Element Solutions of Non-Rational B-Spline and ANCF Elements in the Analysis of Flexible Multibody Systems." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47349.

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In this investigation, comparison of finite element solutions obtained using the B-spline approach and the absolute nodal coordinate formulation (ANCF) is performed. Furthermore, equivalence of the two formulations with different orders of polynomials and degrees of continuity is demonstrated by several numerical examples. The degree of continuity can be easily controlled in B-spline elements by changing knot multiplicities, while continuity conditions associated with higher order derivatives need to be imposed to achieve C2 and higher continuities in ANCF elements. In order to compare element
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Jeong, Myeong-Ju, and Chan-Young Park. "Polynomial invariants and Vassiliev invariants." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2002. http://dx.doi.org/10.2140/gtm.2002.4.89.

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Ricca, Renzo L. "Vortex knot cascade in polynomial skein relations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4951930.

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