ON THE STRUCTURE AND SCARCITY OF ALTERNATING LINKS AND TANGLES
Morwen B. Thistlethwaite · Journal of Knot Theory and Its Ramifications · 1998
It is shown that the proportion of alternating n-crossing, prime link types amongst all n-crossing prime link types tends to zero exponentially with increasing n. Also, a characterization is established for essential annuli in alternating tangles, and a simple criterion is given for equivalence of alternating tangles.