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- LOTHAR GERRITZEN, RALF HOLTKAMP
- 2002

Generalizations of the series exp and log to noncommutative non-associative 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) = EXPˆ⊗EXP where EXP is… (More)

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

- 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) T = S T S x S for powers relative to T is derived. Similarly binomial coefficients T S,V of the second kind are introduced and it is shown that (x ⊗ 1 + 1 ⊗ x) T =… (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 ˆ a(t) := a(t) 2 n−1 · n−1 i=1 (2 i − 1) is an integer which is a product of Mersenne binomials. One obtains summation… (More)

- 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)

- Lothar Gerritzen
- 2005

- 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)

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