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

  • Andrew Elvey Price
  • Alan D. Sokal
DOI: https://doi.org/10.37236/9571

Abstract

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.

Published
2020-10-16
Issue
Volume 27, Issue 4 (2020)
Article Number
P4.6