A Burnside-process algorithm generates uniformly random Pólya trees in near-linear time, supported by a new product formula for permutation-invariant labeled trees.
Martin, The Foata-Fuchs proof of Cayley’s formula, and 24 LAURENT BARTHOLDI AND PERSI DIACONIS its probabilistic uses , Electron
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An algorithm for uniform generation of unlabeled trees (P\'olya trees), with an extension of Cayley's formula
A Burnside-process algorithm generates uniformly random Pólya trees in near-linear time, supported by a new product formula for permutation-invariant labeled trees.