Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
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DOI：
10.37236/9571
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发表时间：
2020-10-16
影响因子：
0.7
通讯作者：
Sokal, Alan D.
中科院分区：
文献类型：
--
作者：
Price, Andrew Elvey;Sokal, Alan D.
我们找到了沃德多项式的普通生成函数的 Thron 型连分数（T 分数），以及使用大量（实际上是无限）独立不定式族的一些概括。我们的证明基于超级增强完美匹配和标记 Schroder 路径之间的双射，它概括了完美匹配和标记 Dyck 路径之间的 Flajolet 双射。
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 Schroder paths, which generalizes Flajolet's bijection between perfect matchings and labeled Dyck paths.