Geodesic
Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Andrew Elvey Price1 ; Alan D. Sokal2
1LaBRI, Université de Bordeaux
2New York University
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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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.
DOI : 10.37236/9571
Classification : 05C78, 05C38, 05A19, 05A10, 05A15, 05A18, 92D15
Mots-clés : generating function of the Ward polynomials, perfect matchings, labeled Dyck paths.

Andrew Elvey Price  1   ; Alan D. Sokal  2

1 LaBRI, Université de Bordeaux
2 New York University 
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     author = {Andrew Elvey Price and Alan D. Sokal},
     title = {Phylogenetic trees, augmented perfect matchings, and a {Thron-type} continued fraction {(T-fraction)} for the {Ward} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9571},
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Andrew Elvey Price; Alan D. Sokal. Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9571

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