Editing Knot theory (section)

===Alexander–Briggs notation===<!--this section is linked to from locations including [[Template:Infobox knot theory]]-->
This is the most traditional notation, due to the 1927 paper of [[James Waddell Alexander II|James W. Alexander]] and [[Garland Baird Briggs|Garland B. Briggs]] and later extended by [[Dale Rolfsen]] in his knot table (see image above and [[List of prime knots]]). The notation simply organizes knots by their crossing number. One writes the crossing number with a subscript to denote its order amongst all knots with that crossing number. This order is arbitrary and so has no special significance (though in each number of crossings the [[twist knot]] comes after the [[torus knot]]). Links are written by the crossing number with a superscript to denote the number of components and a subscript to denote its order within the links with the same number of components and crossings. Thus the trefoil knot is notated 3<sub>1</sub> and the Hopf link is 2{{sup sub|2|1}}.  Alexander–Briggs names in the range 10<sub>162</sub> to 10<sub>166</sub> are ambiguous, due to the discovery of the [[Perko pair]] in [[Charles Newton Little]]'s original and subsequent knot tables, and differences in approach to correcting this error in knot tables and other publications created after this point.<ref>"[http://richardelwes.co.uk/2013/08/14/the-revenge-of-the-perko-pair/ The Revenge of the Perko Pair]", ''RichardElwes.co.uk''. Accessed February 2016. Richard Elwes points out a common mistake in describing the Perko pair.</ref>