Stick Numbers of Links with Two Trivial Components

A knot is an embedding of S in S, and a link is an embedding of one or more copies of S in S. The number of copies of S is called the number of components of the link. We usually think of a link as made out of string, but we can also think of the link as made up of line segments, which we call sticks, which can connect at any angle, but cannot bend. We would like to know the minimum number of sticks required to make any given link, or alternatively, which links can be made with a given number of sticks and no fewer. We call the minimum number of sticks required to make a link the stick number of the link, denoted s(L). Here we give a proof that there is only one link with s(L) = 7 and several lemmas which may eventually lead to a classification of the links with s(L) = 8.