{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:22:14Z","timestamp":1759335734685},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>Let<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548307008425_inline1\"><jats:alt-text>$\\Tn{}$<\/jats:alt-text><\/jats:inline-graphic>denote the set of unrooted labelled trees of size<jats:italic>n<\/jats:italic>and let \u2133 be a particular (finite, unlabelled) tree. Assuming that every tree of<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548307008425_inline1\"><jats:alt-text>$\\Tn{}$<\/jats:alt-text><\/jats:inline-graphic>is equally likely, it is shown that the limiting distribution as<jats:italic>n<\/jats:italic>goes to infinity of the number of occurrences of \u2133 is asymptotically normal with mean value and variance asymptotically equivalent to<jats:italic>\u03bcn<\/jats:italic>and \u03c3<jats:sup>2<\/jats:sup><jats:italic>n<\/jats:italic>, respectively, where the constants \u03bc&gt;0 and \u03c3\u22650 are computable.<\/jats:p>","DOI":"10.1017\/s0963548307008425","type":"journal-article","created":{"date-parts":[[2007,9,28]],"date-time":"2007-09-28T14:05:22Z","timestamp":1190988322000},"page":"21-59","source":"Crossref","is-referenced-by-count":12,"title":["The Distribution of Patterns in Random Trees"],"prefix":"10.1017","volume":"17","author":[{"given":"FR\u00c9D\u00c9RIC","family":"CHYZAK","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MICHAEL","family":"DRMOTA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"THOMAS","family":"KLAUSNER","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GERARD","family":"KOK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,1,1]]},"reference":[{"key":"S0963548307008425_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(75)90076-X"},{"key":"S0963548307008425_ref14","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1978-085-0"},{"key":"S0963548307008425_ref1","unstructured":"[1] Aho A. 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