Title: Some Distributions on Finite Rooted Binary Trees,
Abstract: We introduce some natural families of distributions on rooted binary ranked
plane trees with a view toward unifying ideas from various fields, including
macroevolution, epidemiology, computational group theory, search algorithms and
other fields. In the process we introduce the notions of split-exchangeability
and plane-invariance of a general Markov splitting model in order to readily
obtain probabilities over various equivalence classes of trees that arise in
statistics, phylogenetics, epidemiology and group theory.