Phylogenetic Trees, Augmented Perfect Matchings, and a Thron-type Continued Fraction (T-fraction) for the Ward Polynomials

  • Andrew Elvey Price
  • Alan D. Sokal


We find a Thron-type continued fraction (T-fraction) for the ordinary generating function of the Ward polynomials, as well as for some generalizations employing a large (indeed infinite) family of independent indeterminates. Our proof is based on a bijection between super-augmented perfect matchings and labeled Schröder paths, which generalizes Flajolet's bijection between perfect matchings and labeled Dyck paths.

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