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- Lothar Gerritzen
- J. Symb. Comput.
- 2006

- LOTHAR GERRITZEN, RALF HOLTKAMP
- 2002

Generalizations of the series exp and log to noncommutative nonassociative and other types of algebras were regarded by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x) exp(x) = exp(2x), exp(0) = 1. We call the unique series H = H(x, y) in two non-associative… (More)

- L Gerritzen
- 2005

In this note we introduce the concept of a shuffle product ⊔⊔ for planar tree polynomials and give a formula to compute the planar shuffle product S ⊔⊔ T of two finite planar reduced rooted trees S, T. It is shown that ⊔⊔ is dual to the co-addition ∆ which leads to a formula for the coefficients of ∆(f). It is also proved that ∆(EXP ) = EXP ⊗̂EXP where EXP… (More)

- Hans Ulrich Simon, Lothar Gerritzen, +10 authors Shafi Goldwasser
- 2003

Acknowledgments First of all it is a pleasure to thank my supervisor Hans Ulrich Simon for the great support and the nice atmosphere in his research group. He has been a reliable source of encouragement and adv ice through all my years at the Ruhr-Universität Bochum. Thanks also to all the nice people I met at the " Lehrstuhl für Mathematik und Informatik "… (More)

- Lothar Gerritzen
- 2005

The notion of binomial coefficients (T S ) of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) = ∑

- Lothar Gerritzen
- 2005

- L. Gerritzen
- 2005

A planar monomial is by definition an isomorphism class of a finite, planar, reduced rooted tree. If x denotes the tree with a single vertex, any planar monomial is a non-associative product in x relative to m−array grafting. A planar power series f(x) over a field K in x is an infinite sum of K−multiples of planar monomials including the unit monomial… (More)

- L Gerritzen
- 2005

The non-associative exponential series exp(x) is a power series with monomials from the magma M of finite, planar rooted trees. The coefficient a(t) of exp(x) relative to a tree t of degree n is a rational number and it is shown that â(t) := a(t) 2n−1 · ∏n−1 i=1 (2 i − 1) is an integer which is a product of Mersenne binomials. One obtains summation formulas

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