{"paper":{"title":"The Distribution of Patterns in Random Trees","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Fr\\'ed\\'eric Chyzak (INRIA Rocquencourt), Gerard Kok, Michael Drmota, Thomas Klausner","submitted_at":"2006-05-05T09:31:01Z","abstract_excerpt":"Let $T\\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to infinity of the number of occurrences of $M$ as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to $\\mu n$ and $\\sigma^2n$, respectively, where the constants $\\mu>0$ and $\\sigma\\ge 0$ are computable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0605019","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}