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The planar Tree Lagrange Inversion Formula
Lothar Gerritzen
A planar tree power series over a field is a formal expression where the sum is extended over all isomorphism classes of finite planar reduced rooted trees…
Planar Binomial Coefficients
Lothar Gerritzen
The notion of binomial coefficients of finite planar, reduced rooted trees is defined and a recursive formula for its computation is shown. The nonassociative…
Mersenne Binomials and the Coefficients of the non-associative Exponential
Lothar Gerritzen
The non-associative exponential series is a power series with monomials from the magma of finite, planar rooted trees. The coefficient of relative to a…
Planar Shuffle Product, Co-Addition and the non-associative Exponential
Lothar Gerritzen
In this note we introduce the concept of a shuffle product $\sq$ for planar tree polynomials and give a formula to compute the planar shuffle product $S \ \sq T$ of two finite plan…
The planar Chain Rule and the Differential Equation for the planar Logarithms
Lothar Gerritzen
A planar monomial is by definition an isomorphism class of a finite, planar, reduced rooted tree. If denotes the tree with a single vertex, any planar monomial is a non-associa…