抄録
We introduce an algorithm for generating all generically immersed intervals in the unit disk with a given number of double points N and modulo mirror images. These interval immersions, known as free divides, are associated with knots via a particular map into the 3-sphere, and the gordian unknotting number of a link of a free divide is equal the number of double points of the immersion. So the algorithm provides access to knots for which the gordian number is explicitly known. A computer implementation of our algorithm is described, and we report the results for the total numbers of free divides for N ≤ 8.
