EUDML

We study $(𝒜, +, \oplus)$ , the ring of arithmetical functions with unitary convolution, giving an isomorphism between $(𝒜, +, \oplus)$ and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring $(𝒜, +, \cdot)$ of arithmetical functions with Dirichlet convolution and the power series ring $[[x_{1}, x_{2}, x_{3}, \dots]]$ on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization into atoms...

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The maximal spectral radius of a digraph with ${(m + 1)}^{2} - s$ edges.

Truncations of the ring of number-theoretic functions.

On some partial orders associated to generic initial ideals.

A conjecture on Poincaré-Betti series of modules of differential operators on a generic hyperplane arrangement.

Standard paths in another composition poset.

Enumeration of concave integer partitions.

Some conjectures about the Hilbert series of generic ideals in the exterior algebra.

The ring of arithmetical functions with unitary convolution: Divisorial and topological properties