{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:50:24Z","timestamp":1754110224396,"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>We study fringe subtrees of random $m$-ary search trees and of  preferential attachment trees, by putting them in the context of generalised P\u00f3lya urns. In particular we show that for the random $m$-ary search trees with $ m\\leq 26 $ and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree $ T $ converges to a normal distribution;  more generally, we also prove multivariate normal distribution results for random vectors of such numbers for different fringe subtrees. Furthermore, we show that the number of protected nodes in random $m$-ary search trees for $m\\leq 26$ has asymptotically a normal distribution.<\/jats:p>","DOI":"10.37236\/6374","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:54:05Z","timestamp":1578671645000},"source":"Crossref","is-referenced-by-count":9,"title":["Multivariate Normal Limit Laws for the Numbers of Fringe Subtrees in $m$-ary Search Trees and Preferential Attachment Trees"],"prefix":"10.37236","volume":"24","author":[{"given":"Cecilia","family":"Holmgren","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Svante","family":"Janson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matas","family":"Sileikis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2017,6,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:55:59Z","timestamp":1579236959000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,30]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6374","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,6,30]]},"article-number":"P2.51"}}