The planar Tree Lagrange Inversion Formula
| dc.creator | Gerritzen, Lothar | |
| dc.date | 2005-02-17 | |
| dc.date.accessioned | 2026-07-07T05:17:07Z | |
| dc.date.available | 2026-07-07T05:17:07Z | |
| dc.description | A planar tree power series over a field $K$ is a formal expression $$\sum c_T \cdot T$$ where the sum is extended over all isomorphism classes of finite planar reduced rooted trees $T$ and where the coefficients $c_T$ are in $K$. Mulitplications of these power series is induced by planar grafting of trees and turns the K-vectorspace $K\{x\}_\infty$ of those power series into an algebra, see [G]. If $f \in K \{x\}_\infty$ there is a unique $g(x) \in K \{x\}_\infty$ of order $> 0$ such that $$ g(x) = x \cdot f(g(x))$$ where $f(g(x))$ is obtained by substituting $g(x)$ for $x$ in $f(x).$ Formulas for the coefficients of $g$ in terms of the coefficients of $f$ are obtained by the use of the planar tree Lukaciewicz language. This result generalizes the classical Lagrange inversion formula, see [C],[R],[Sch]. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502381 | |
| dc.identifier | http://arxiv.org/abs/math/0502381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74235 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17A50 | |
| dc.title | The planar Tree Lagrange Inversion Formula | |
| dc.type | text |