  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.
