Some combinatorial properties of the Hurwitz series ring

2017/10/16 by Barbero, Stefano, Cerruti, Umberto, Murru, Nadir
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.05665

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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