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But this does not imply that universal cycles (or ucycles) exist, since vertices represent equivalence classes of partitions! We use this result to prove, however, that ucycles of ${\\cal P}(n,k)$ exist for all $n \\geq 3$ when $k=2$. We reprove that they exist for odd $n$ when $k = n-1$ and that they do not exist for even $n$ when $k = n-1$. 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