{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:20Z","timestamp":1753893860690,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study universal cycles of the set $\\mathcal{P}(n,k)$ of $k$-partitions of the set $[n]:=\\{1,2,\\ldots,n\\}$ and prove that the transition digraph associated with $\\mathcal{P}(n,k)$ 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 $\\mathcal{P}(n,k)$ exist for all $n \\geq 3$ 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 ${{n-2}\\brace{k-2}}$ is odd ($3 \\leq k &lt; n-1$). We also show that there exist universal cycles of partitions of $[n]$ into $k$ subsets of distinct sizes when $k$ is sufficiently smaller than $n$, and therefore that there exist universal packings of the partitions in $\\mathcal{P}(n,k)$. An analogous result for coverings completes the investigation.\u00a0\u00a0 <\/jats:p>","DOI":"10.37236\/5051","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:22:19Z","timestamp":1578694939000},"source":"Crossref","is-referenced-by-count":1,"title":["Universal and Near-Universal Cycles of Set Partitions"],"prefix":"10.37236","volume":"22","author":[{"given":"Zach","family":"Higgins","sequence":"first","affiliation":[]},{"given":"Elizabeth","family":"Kelley","sequence":"additional","affiliation":[]},{"given":"Bertilla","family":"Sieben","sequence":"additional","affiliation":[]},{"given":"Anant","family":"Godbole","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,12,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p48\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p48\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:07:36Z","timestamp":1579255656000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p48"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,23]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5051","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,12,23]]},"article-number":"P4.48"}}