ON UNIVERSAL CYCLES FOR K-SUBSETS OF AN N-SET

A universal cycle, or Ucycle, for k-subsets of [n] = {1,..., n} is a cyclic sequence of ((n)(k)) integers with the property that each subset of [n] of size k appears exactly once consecutively in the sequence. Chung, Diaconis, and Graham have conjectured their existence for fixed k and large n when n\((n)(k)). Here the Ucycles for k = 3, 4, 6 and large n relatively prime to k are exhibited.