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NearUniversal Cycles for Subsets Exist
, 2008
"... Let S be a cyclic nary sequence. We say that S is a universal cycle ((n,k)Ucycle) for ksubsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation to pa ..."
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Let S be a cyclic nary sequence. We say that S is a universal cycle ((n,k)Ucycle) for ksubsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation
NearUniversal Cycles for Subsets Exist
, 2009
"... Let S be a cyclic nary sequence. We say that S is a universal cycle ((n, k)Ucycle) for ksubsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation to p ..."
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Let S be a cyclic nary sequence. We say that S is a universal cycle ((n, k)Ucycle) for ksubsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation
Universal and NearUniversal Cycles of Set Partitions
"... We study universal cycles of the set P(n, k) of kpartitions of the set [n]:= {1, 2,..., n} and prove that the transition digraph associated with P(n, k) is Eulerian. But this does not imply that universal cycles (or ucycles) exist, since vertices represent equivalence classes of partitions. We use ..."
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We study universal cycles of the set P(n, k) of kpartitions of the set [n]:= {1, 2,..., n} and prove that the transition digraph associated with P(n, k) is Eulerian. But this does not imply that universal cycles (or ucycles) exist, since vertices represent equivalence classes of partitions. We