We study universal cycles of the set P(n,k) of k-partitions 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 this result to prove, however, that ucycles of P(n,k) exist for all n≥3 when k=2. We reprove that they exist for odd n when k=n−1 and that they do not exist for even n when k=n−1. An infinite family of (n,k) for which ucycles do not exist is shown to be those pairs for which (Formula presented) is odd (3≤k
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16610 |
| Date | 23 December 2015 |
| Creators | Higgins, Zach, Kelley, Elizabeth, Sieben, Bertilla, Godbole, Anant |
| 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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