Research Article

Recurrence Relations for Knot Polynomials of Twist Knots

Volume: 4 Number: 1 March 1, 2021
EN

Recurrence Relations for Knot Polynomials of Twist Knots

Abstract

This paper gives HOMFLY polynomials and Kauffman polynomials L and F of twist knots as recurrence relations, respectively, and also provides some recursive properties of them.

Keywords

References

  1. [1] J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc., 30 (1928), 275–308.
  2. [2] J. H. Conway, An enumeration of knots and kinks, and some of their algebraic properties, in Computational Problems in Abstract Algebra, (Pergamon, Oxford, 1970), 329–358.
  3. [3] S. Friedl, S. Vidussi, A Survey of Twisted Alexander Polynomials, M. Banagl, D. Vogel (eds), The Mathematics of Knots. Contributions in Mathematical and Computational Sciences, Springer, Berlin, 2011, pp. 45–94.
  4. [4] İ. Altıntaş, K. Taşköprü, A generalization of the Alexander polynomial, Int. J. Math. Comb., 4 (2016), 21–28.
  5. [5] İ. Altıntaş, K. Taşköprü, A generalization of the Alexander polynomial as an application of the delta derivative, Turk. J. Math., 42(2) (2018), 515–527.
  6. [6] V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., 12 (1985), 103–111.
  7. [7] L. H. Kauffman, State models and the Jones polynomial, Topology, 26 (1987), 395–407.
  8. [8] İ. Altıntaş, An oriented state model for the Jones polynomial and its applications alternating links, Appl. Math. Comput., 194(1) (2007), 168–178.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

March 1, 2021

Submission Date

January 8, 2021

Acceptance Date

March 17, 2021

Published in Issue

Year 2021 Volume: 4 Number: 1

APA
Taşköprü, K., & Sinan, Z. Ş. (2021). Recurrence Relations for Knot Polynomials of Twist Knots. Fundamental Journal of Mathematics and Applications, 4(1), 59-66. https://doi.org/10.33401/fujma.856647
AMA
1.Taşköprü K, Sinan ZŞ. Recurrence Relations for Knot Polynomials of Twist Knots. Fundam. J. Math. Appl. 2021;4(1):59-66. doi:10.33401/fujma.856647
Chicago
Taşköprü, Kemal, and Zekiye Şevval Sinan. 2021. “Recurrence Relations for Knot Polynomials of Twist Knots”. Fundamental Journal of Mathematics and Applications 4 (1): 59-66. https://doi.org/10.33401/fujma.856647.
EndNote
Taşköprü K, Sinan ZŞ (March 1, 2021) Recurrence Relations for Knot Polynomials of Twist Knots. Fundamental Journal of Mathematics and Applications 4 1 59–66.
IEEE
[1]K. Taşköprü and Z. Ş. Sinan, “Recurrence Relations for Knot Polynomials of Twist Knots”, Fundam. J. Math. Appl., vol. 4, no. 1, pp. 59–66, Mar. 2021, doi: 10.33401/fujma.856647.
ISNAD
Taşköprü, Kemal - Sinan, Zekiye Şevval. “Recurrence Relations for Knot Polynomials of Twist Knots”. Fundamental Journal of Mathematics and Applications 4/1 (March 1, 2021): 59-66. https://doi.org/10.33401/fujma.856647.
JAMA
1.Taşköprü K, Sinan ZŞ. Recurrence Relations for Knot Polynomials of Twist Knots. Fundam. J. Math. Appl. 2021;4:59–66.
MLA
Taşköprü, Kemal, and Zekiye Şevval Sinan. “Recurrence Relations for Knot Polynomials of Twist Knots”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 1, Mar. 2021, pp. 59-66, doi:10.33401/fujma.856647.
Vancouver
1.Kemal Taşköprü, Zekiye Şevval Sinan. Recurrence Relations for Knot Polynomials of Twist Knots. Fundam. J. Math. Appl. 2021 Mar. 1;4(1):59-66. doi:10.33401/fujma.856647

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