Distributions on bicoloured binary trees arising from the principle of parsimony (Q1208487)

The paper investigates the distribution of binary trees with bicoloured endpoints under the taxonomic principle of parsimony. A formula given by \textit{M. Carter}, \textit{M. Hendy}, \textit{D. Penny}, \textit{L. A. Székely} and \textit{N. C. Wormald} [SIAM J. Discrete Math. 3, No. 1, 38-47 (1990; Zbl 0705.05017)] for the number of binary trees with given number of endpoints in two colours and given weight (= number of mutations) is proved in a more constructive way than by Carter et al. A generalization for \(r\)-coloured trees is outlined. Dually the author also counts bicolourings of given weight on given binary trees in order to calculate mean and variance for the weight of aligned binary-state sequence data.