Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
| Autor: | Alan D. Sokal, Andrew Elvey Price |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
05A19 (Primary)
05A10 05A15 05A18 30B70 92B10 (Secondary) Mathematics::Combinatorics Phylogenetic tree Applied Mathematics Generating function Type (model theory) Theoretical Computer Science Combinatorics Computational Theory and Mathematics Bijection FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Fraction (mathematics) Geometry and Topology Combinatorics (math.CO) Mathematics |
| Zdroj: | Electronic Journal of Combinatorics |
| DOI: | 10.48550/arxiv.2001.01468 |
| Popis: | 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. Comment: 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) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|