A universal cycle (u-cycle) is a compact listing of a collection of combinatorial objects. In this paper, we use natural encodings of these objects to show the existence of u-cycles for collections of subsets, restricted multisets, and lattice paths. For subsets, we show that a u-cycle exists for the κ-subsets of an n-set if we let κ vary in a non zero length interval. We use this result to construct a "covering" of length (1+o(1))(n/κ) for all subsets of [n] of size exactly κ with a specific formula for the o(1) term. We also show that u-cycles exist for all n-length words over some alphabet ∑, which contain all characters from R ⊂ ∑. Using this result we provide u-cycles for encodings of Sperner families of size 2 and proper chains of subsets.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-17737 |
| Date | 01 December 2011 |
| Creators | Blanca, Antonio, Godbole, Anant P. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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