A DeepMind collaboration used machine-learning methods to guide the discovery and proof of a relationship between the natural slope of a knot
and its signature (Davies et al. 2021).
Knot signatures are implemented in the Wolfram Language as KnotData[knot,
"Signature"]. The following table summarizes knot signatures for
knots on 10 of fewer crossings.
Davies, A. et al. "Advancing Mathematics by Guiding Human Intuition with AI." Nature600, 70-74, 2021. https://doi.org/10.1038/s41586-021-04086-x.Gordon,
C. M.; Litherland, R. A.; and Murasugi, K. "Signatures of Covering
Links." Canad. J. Math.33, 381-394, 1981.Murasugi,
K. "On the Signature of Links." Topology9, 283-298, 1970.Murasugi,
K. "Signatures and Alexander Polynomials of Two-Bridge Knots." C. R.
Math. Rep. Acad. Sci. Canada5, 133-136, 1983.Murasugi, K.
"On the Signature of a Graph." C. R. Math. Rep. Acad. Sci. Canada10,
107-111, 1988.Murasugi, K. "On Invariants of Graphs with Applications
to Knot Theory." Trans. Amer. Math. Soc.314, 1-49, 1989.Rolfsen,
D. Knots
and Links. Wilmington, DE: Publish or Perish Press, 1976.Stoimenow,
A. "Signatures." https://stoimenov.net/stoimeno/homepage/ptab/sig10.html.
of a knot 
can be defined using the skein
relationship
is the Conway polynomial and 
is an odd number.
