{"paper":{"title":"The asymptotic number of different rooted trees of a tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xueliang Li, Yiyang Li, Yongtang Shi","submitted_at":"2012-07-17T08:44:04Z","abstract_excerpt":"Let $\\mathcal{T}_n$ be the set of trees with $n$ vertices. Suppose that each tree in $\\mathcal{T}_n$ is equally likely. We show that the number of different rooted trees of a tree equals $(\\mu_r+o(1))n$ for almost every tree of $\\mathcal{T}_n$, where $\\mu_r$ is a constant. As an application, we show that the number of any given pattern in $\\mathcal{T}_n$ is also asymptotically normally distributed with mean $\\sim \\mu_M n$ and variance $\\sim \\sigma_M n$, where $\\mu_M, \\sigma_M$ are some constants related to the given pattern. This solves an open question claimed in Kok's thesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3915","kind":"arxiv","version":2},"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"}