{"paper":{"title":"Capturing a phylogenetic tree when the number of character states varies with the number of leaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Mike Steel","submitted_at":"2015-03-03T05:49:54Z","abstract_excerpt":"We show that for any two values $\\alpha, \\beta >0 $ for which $\\alpha+\\beta>1$ then there is a value $N$ so that for all $n \\geq N$ the following holds. For any binary phylogenetic tree $T$ on $n$ leaves there is a set of $\\lfloor n^\\alpha \\rfloor$ characters that capture $T$, and for which each character takes at most $\\lfloor n^\\beta \\rfloor$ distinct states. Here `capture' means that $T$ is the unique perfect phylogeny for these characters. Our short proof of this combinatorial result is based on the probabilistic method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00831","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"}