{"paper":{"title":"Recovering a tree from the lengths of subtrees spanned by a randomly chosen sequence of leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Lanoue, Steven N. Evans","submitted_at":"2015-06-03T00:29:38Z","abstract_excerpt":"Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \\le k \\le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, \"Can $T$ be identified (up to isomorphism) by the joint probability distribution of the random vector $(W_2, \\ldots, W_n)$?\" We show that if $T$ is known {\\em a priori} to belong to one of various families of edge-weighted trees, then the answer is, \"Yes.\" These families include the edge-weighted trees with edge-weights in general position, the ultrametric edge-weighted "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01091","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"}