a1 Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.
A fundamental and interesting question in knot theory is:
Question 1. How many prime knots of n crossings are there ?
Over time, knot theorists have answered this question for n ≤ 13 by the method of exhaustion: one writes down a list of all possible knots of n crossings, and then works hard to eliminate duplications from the list . A perhaps easier question is the following:
(Received July 17 1986)
(Revised January 26 1987)