KnotData Source Information

KnotData is based on a wide range of sources, with enhancement at the Wolfram Research Companies by both human and algorithmic processing.

Among principal sources for KnotData are:

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): 779803.

Burde, G. and H. Zieschang. Knots. Walter de Gruyter, 2003.

Cha, J. C. and Livingston, C. "KnotInfo: Table of Knot Invariants." 2008. »

Fox, R. H. "A Quick Trip Through Knot Theory." In Topology of 3-manifolds and Related Topics (Proc. The Univ. of Georgia Institute, 1961), 119167, 1962.

Garoufalidis, S. "Does the Jones Polynomial Determine the Signature of a Knot?" 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): 3348.

Jones, V. F. R. "Hecke Algebra Representations of Braid Groups and Link Polynomials." Annals of Mathematics. Second Series 126, no. 2 (1987): 335388.

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): 773826.

Kuiper, N. H. "A New Knot Invariant." Mathematische Annalen 278, no. 1-4 (1987): 193209.

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): 735742.

Murasugi, K. "On the Braid Index of Alternating Links." Transactions of the American Mathematical Society 326, no. 1 (1991): 237260.

Orevkov, S. Y. "Classification of Flexible M-Curves of Degree 8 up to Isotopy." Geometric and Functional Analysis 12, no. 4 (2002): 723755.

Rawdon, E. J. and R. G. Scharein. "Upper Bounds for Equilateral Stick Numbers." In Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3 (Las Vegas, NV, 2001). Amer. Math. Soc. Contemp. Math. 5575, 2002.

Rolfsen, D. Knots and Links. Publish or Perish Inc, 1990.

Weisstein, E. W. "MathWorld: A Wolfram Web Resource." 2008. »

Willerton, S. "On the First Two Vassiliev Invariants." Experimental Mathematics 11, no. 2 (2002): 289296.

Williams, R. F. "The Braid Index of Generalized Cables." Pacific Journal of Mathematics 155, no. 2 (1992): 369375.

To report an error or suggest an addition to KnotData, contact the Wolfram Research KnotData team.