I am writing a small paper on Knot Theory for my undergrad geometry course and I have a question about the tabulation of knots. The books I have discuss the different notations, except for the ALexander and Briggs notation, which is used in the tables provided in the appendices. I believe I understand the notation, but I want to be sure. [tex]4_1[/tex] which refers to the figure eight knot means that this is the first knot of the class of knots that has 4 crossings that cannot be undone by Reidemeister moves. correct? If that is the case, then in the set of knots with 8 fundamental crossings, is there any significance to their ordering in the table? could I take [tex]8_1[/tex] and [tex]8_2[/tex] and just switch their corresponding knots? also, on some of the knots, there is a superscript. what is the significance of that? Thanks.