Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Combinatorics
2021-02-24 v2
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 Schr\"oder paths, which generalizes Flajolet's bijection between perfect matchings and labeled Dyck paths.
Keywords
Cite
@article{arxiv.2001.01468,
title = {Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials},
author = {Andrew Elvey Price and Alan D. Sokal},
journal= {arXiv preprint arXiv:2001.01468},
year = {2021}
}
Comments
LaTeX2e, 36 pages (includes 4 figures). Version 2 corrects a small error in the definition of crossing number (p. 6) and includes a proof of the previously conjectured (1.25)/(1.26)