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arXiv · 1710.05665

Some combinatorial properties of the Hurwitz series ring

Stefano Barbero·Umberto Cerruti·Nadir Murru
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Abstract

We study some properties and perspectives of the Hurwitz series ring $H_R[[t]]$, for a commutative ring with identity $R$. Specifically, we provide a closed form for the invertible elements by means of the complete ordinary Bell polynomials, we highlight some connections with well--known transforms of sequences, and we see that the Stirling transforms are automorphisms of $H_R[[t]]$. Moreover, we focus the attention on some special subgroups studying their properties. Finally, we introduce a new transform of sequences that allows to see one of this subgroup as an ultrametric dynamic space.

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Stefano Barbero, Umberto Cerruti, Nadir Murru. 2017-10-16. Some combinatorial properties of the Hurwitz series ring. https://arxiv.org/abs/1710.05665

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