{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833055,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A $k$-universal permutation, or $k$-superpermutation, is a permutation that contains all permutations of length $k$ as patterns.\u00a0 The problem of finding the minimum length of a $k$-superpermutation has recently received significant attention in the field of permutation patterns.\u00a0 One can ask analogous questions for other classes of objects.\u00a0 In this paper, we study $k$-supertrees.\u00a0 For each $d\\geq 2$, we focus on two types of rooted plane trees called $d$-ary plane trees and $[d]$-trees.\u00a0 Motivated by recent developments in the literature, we consider \"contiguous\" and \"noncontiguous\" notions of pattern containment for each type of tree.\u00a0 We obtain both upper and lower bounds on the minimum possible size of a $k$-supertree in three cases; in the fourth, we determine the minimum size exactly.\u00a0 One of our lower bounds makes use of a recent result of Albert, Engen, Pantone, and Vatter on $k$-universal layered permutations.<\/jats:p>","DOI":"10.37236\/8971","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T03:25:16Z","timestamp":1588821916000},"source":"Crossref","is-referenced-by-count":0,"title":["Supertrees"],"prefix":"10.37236","volume":"27","author":[{"given":"Colin","family":"Defant","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noah","family":"Kravitz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashwin","family":"Sah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,4,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p7\/8064","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p7\/8064","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T03:25:16Z","timestamp":1588821916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/8971","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,4,17]]},"article-number":"P2.7"}}