Enumerating the Prime Alternating Links
  This is the third paper in a series devoted to enumerating the prime alternating knots and links. This paper establishes a method for enumerating the prime alternating links. It is shown that one may choose any prime alternating link diagram of a given minimal crossing size and by applications of just two operators (T and OTS, introduced in the first paper in the series, Enumerating the Prime Alternating Knots, Part I) to the selected seed link, one obtains all prime alternating link diagrams of the desired minimal crossing size. 
Stuart Rankin and Ortho Smith