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Phylogenetic trees, augmented perfect matchings, and a thron-type continued fraction (T-fraction) for the ward polynomials

Price, AE; Sokal, AD; (2020) Phylogenetic trees, augmented perfect matchings, and a thron-type continued fraction (T-fraction) for the ward polynomials. Electronic Journal of Combinatorics , 27 (4) , Article P4.6. 10.37236/9571. Green open access

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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.

Type: Article
Title: Phylogenetic trees, augmented perfect matchings, and a thron-type continued fraction (T-fraction) for the ward polynomials
Open access status: An open access version is available from UCL Discovery
DOI: 10.37236/9571
Language: English
Additional information: ©The authors. Released under the CC BY-ND license (International 4.0) https://creativecommons.org/licenses/by-nc/4.0/
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10112439
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