Knot data source information

Primary source:

Wolfram|Alpha Knowledgebase, 2021.

Background sources and references:

  • Adams, C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. W. H. Freeman, 1994.
  • Alvarez, M. and J. Labastida. "Vassiliev Invariants for Torus Knots." Journal of Knot Theory and Its Ramifications 5, no. 6 (1996): 779-803.
  • Burde, G. and H. Zieschang. Knots. Walter de Gruyter, 2003.
  • Fox, R. H. "A Quick Trip through Knot Theory." In Topology of 3-Manifolds and Related Topics: (Proceedings of the University of Georgia Institute, 1961) [Fort, M. K. (Ed.)], Prentice Hall, 119-167, 1962.
  • Garoufalidis, S. "Does the Jones Polynomial Determine the Signature of a Knot?" arXiv:math/0310203v1 (2003). »
  • Hoehn, S. "Color-by-Number: An Exploration of Knot Colorings." Thesis, Xavier University, 2005.
  • Hoste, J. and M. Thistlethwaite. "The First 1,701,936 Knots." Mathematical Intelligencer 20, no. 4 (1998): 33-48.
  • Jones, V. F. R. "Hecke Algebra Representations of Braid Groups and Link Polynomials." Annals of Mathematics. Second Series 126, no. 2 (1987): 335-388.
  • Kauffman, L. H. On Knots. Princeton University Press, 1987.
  • Kronheimer, P. B. and T. S. Mrowka. "Gauge Theory for Embedded Surfaces. I." Topology, An International Journal of Mathematics 32, no. 4 (1993): 773-826.
  • Kuiper, N. H. "A New Knot Invariant." Mathematische Annalen 278, no. 1-4 (1987): 193-209.
  • Lickorish, W. B. R. An Introduction to Knot Theory. Springer-Verlag, 1997.
  • Livingston, C. "Computations of the Ozsvath-Szabo Knot Concordance Invariant." Geometry and Topology 8 (2004): 735-742.
  • Livingston, C. and J. C. Cha. "Table of Knot Invariants." KnotInfo. »
  • Murasugi, K. "On the Braid Index of Alternating Links." Transactions of the American Mathematical Society 326, no. 1 (1991): 237-260.
  • Orevkov, S. Y. "Classification of Flexible M-Curves of Degree 8 up to Isotopy." Geometric and Functional Analysis 12, no. 4 (2002): 723-755.
  • Rawdon, E. J. and R. G. Scharein. "Upper Bounds for Equilateral Stick Numbers." In Physical Knots: Knotting, Linking, and Folding Geometric Objects in R3 (Las Vegas, NV, 2001). Contemporary Mathematics 55-75, 2002.
  • Rolfsen, D. Knots and Links. Publish or Perish Inc., 1990.
  • Weisstein, E. W. MathWorld—A Wolfram Web Resource. »
  • Willerton, S. "On the First Two Vassiliev Invariants." Experimental Mathematics 11, no. 2 (2002): 289-296.
  • Williams, R. F. "The Braid Index of Generalized Cables." Pacific Journal of Mathematics 155, no. 2 (1992): 369-375.

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