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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.3915","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-17T08:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"85030019b3893ee41ec751f0249775a52338a5b1625dc158222e649157f02c3f","abstract_canon_sha256":"101c41e78a0581d599b787cf13dc031e73ba855ec80d4da11ba1c34d61984362"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:25.719539Z","signature_b64":"q8+9Idn2XfBqCl5MglAZIYUPFeuH4BMRiLRSmMb3T4vOFXLKJQi+bwr2QLh+FkgLyOxUvTxFib7ZJi+k5KiLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1414ba619e559d6fc9349683edd18c4356d86275296b7528e2d88b76eb68336c","last_reissued_at":"2026-05-18T03:25:25.719044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:25.719044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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