  An analysis of extensive simulations of interacting self-avoiding polygons on
cubic lattice shows that the frequencies of different knots realized in a
random, collapsed polymer ring decrease as a negative power of the ranking
order, and suggests that the total number of different knots realized grows
exponentially with the chain length. Relative frequencies of specific knots
converge to definite values because the free energy per monomer, and its
leading finite size corrections, do not depend on the ring topology, while a
subleading correction only depends on the crossing number of the knots.
