On universal cycles for multisets

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