Question about Alexander and Briggs notation

[ComputerGeek]

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.

$$4_1$$ 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 $$8_1$$ and $$8_2$$ and just switch their corresponding knots? also, on some of the knots, there is a superscript. what is the significance of that?

Thanks.

 

[hypermorphism]

In my book (Adams), the superscripts refer to the number of components in the link. I think the subscript is just a historical ordering. For more tables, see the Knot Atlas.