Isomorphism and Symmetries in Random Phylogenetic Trees

2009/12/01 by Miklós Bóna, Philippe Flajolet · 33 citations
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #Mathematics #Phylogenetic tree #Combinatorics #Isomorphism (crystallography) #Homogeneous space #Tree (set theory) #Gaussian #Discrete mathematics #Geometry

paper · pdf · doi:10.1239/jap/1261670685

published in Journal of Applied Probability 46(4), 1005-1019 (Cambridge University Press)

openalex publication_date 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic tree of large size obeys a limiting Gaussian distribution, in the sense of both central and local limits. The probability that two random phylogenetic trees have the same number of symmetries asymptotically obeys an inverse square-root law. Precise estimates for these problems are obtained by methods of analytic combinatorics, involving bivariate generating functions, singularity analysis, and quasi-powers approximations.

Citations

• The variance of the Stirling cycle numbers
• On some problems of a statistical group-theory. IV
• Mathematical Constants

Cited by

• Wedderburn–Etherington number [wikipedia]

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