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Isomorphism and Symmetries in Random Phylogenetic Trees

  • Miklós Bóna (a1) and Philippe Flajolet (a2)

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.

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Copyright

Corresponding author

Postal address: Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611–8105, USA.
∗∗ Postal address: Algorithms Project, INRIA Rocquencourt, F-78153 Le Chesnay, France. Email address: philippe.flajolet@inria.fr

References

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Isomorphism and Symmetries in Random Phylogenetic Trees

  • Miklós Bóna (a1) and Philippe Flajolet (a2)

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