%0 Journal Article
%T Near universal cycles for subsets exist
%A Dawn Curtis
%A Taylor Hines
%A Glenn Hurlbert
%A Tatiana Moyer
%J Mathematics
%D 2008
%I arXiv
%X Let S be a cyclic n-ary sequence. We say that S is a {\it universal cycle} ((n,k)-Ucycle) for k-subsets 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 packings merits investigation. A family {S_n} of (n,k)-Ucycle packings for fixed k is a near-Ucycle if the length of S_n is $(1-o(1))\binom{n}{k}$. In this paper we prove that near-(n,k)-Ucycles exist for all k.
%U http://arxiv.org/abs/0809.3725v1