Alexander-Briggs notation denotes the 
th prime knot having crossing
number 
in a chosen tabulation by 
. Thus 
denotes the trefoil knot,
while 
denotes the figure eight knot. The subscript
specifies the knot's position among the 
-crossing prime knots in that
tabulation and is not a further knot invariant;
consequently, it must be interpreted relative to the stated table.
Alexander and Briggs (1926-1927) used this notation in their extension of the early knot tables. Modern tables retain the notation but correct historical duplications and omissions, including the duplicate ten-crossing knot diagrams now known as the Perko pair.
Rolfsen's widely used table (Rolfsen 2003, Appendix C) retains Alexander-Briggs notation and extends it to links: 
denotes the 
th 
-component link with crossing
number 
.
