On universal cycles for multisets

A Universal Cycle   for tt-multisets of [n]={1,…,n}[n]={1,…,n} is a cyclic sequence of (n+t−1t) integers from [n][n] with the property that each tt-multiset of [n][n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that nn divides (n+t−1t), and it is reasonable to conjecture that this condition is sufficient for large enough nn in terms of tt. We prove the conjecture completely for t∈{2,3}t∈{2,3} and partially for t∈{4,6}t∈{4,6}. These results also support a positive answer to a question of Knuth.