Near universal cycles for subsets exist
| dc.creator | Curtis, Dawn | |
| dc.creator | Hines, Taylor | |
| dc.creator | Hurlbert, Glenn | |
| dc.creator | Moyer, Tatiana | |
| dc.date | 2008-09-22 | |
| dc.date.accessioned | 2026-07-07T10:04:26Z | |
| dc.date.available | 2026-07-07T10:04:26Z | |
| dc.description | 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. | |
| dc.description | 14 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0809.3725 | |
| dc.identifier | http://arxiv.org/abs/0809.3725 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169676 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B30 (Primary) 05A05, 05C45 (Secondary) | |
| dc.title | Near universal cycles for subsets exist | |
| dc.type | text |