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A cyclic sequence of elements of [n] is an (n, k)-Ucycle packing (respectively, (n, k)-Ucycle covering) if every k-subset of [n] appears in this sequence at most once (resp. at least once) as a subsequence of consecutive terms. Let $$p_{n,k}$$pn,k be the length of a longest (n, k)-Ucycle packing and $$c_{n,k}$$cn,k the length of a shortest (n, k)-Ucycle covering. We show that, for a fixed $$k,p_{n,k}={n\\atopwithdelims ()k}-O(n^{\\lfloor k/2\\rfloor })$$k,pn,k=nk-O(nźk/2ź). Moreover, when k is not fixed, we prove that if $$k=k(n)\\le n^{\\alpha }$$k=k(n)≤nź, where $$0

Universal Cycle Packings and Coverings for k-Subsets of an n-Set