Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The growth of the number of prime knots

C. Ernsta1 and D. W. Sumnersa1

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 [12]. A perhaps easier question is the following:

(Received July 17 1986)

(Revised January 26 1987)