  Consider the collection of all t-multisets of {1,...,n}. A universal cycle on
multisets is a string of numbers, each of which is between 1 and n, such that
if these numbers are considered in t-sized windows, every multiset in the
collection is present in the string precisely once. The problem of finding
necessary and sufficient conditions on n and t for the existence of universal
cycles and similar combinatorial structures was first addressed by DeBruijn in
1946 (who considered t-tuples instead of t-multisets). The past 15 years has
seen a resurgence of interest in this area, primarily due to Chung, Diaconis,
and Graham's 1992 paper on the subject. For the case t=3, we determine
necessary and sufficient conditions on n for the existence of universal cycles,
and we examine how this technique can be generalized to other values of t.
