{"paper":{"title":"An algorithm for uniform generation of unlabeled trees (P\\'olya trees), with an extension of Cayley's formula","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.CO","authors_text":"Laurent Bartholdi, Persi Diaconis","submitted_at":"2024-11-26T17:27:09Z","abstract_excerpt":"P\\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with `reality'.\n  Along the way, we give a product formula for the number of rooted labeled trees preserved by a given automorphism; this refines Cayley's formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17613","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17613/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}