27 citations · 92 across the 34 of their papers we have counts for
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Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions
Jan Snellman
We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical functio…
The maximal spectral radius of a digraph with (m+1)^2 - s edges
Jan Snellman
It is known that the spectral radius of a digraph with k edges is \le \sqrt{k}, and that this inequality is strict except when k is a perfect square. For k=m^2 + \ell, \ell fixed,…
Bounds for the Entropy of Graded Algebras
Jan Snellman
Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = \limsup_{n \to \infty} \sqrt[n]{a_n}, where a_n is the vector space dimension of the n'…
The ring of arithmetical functions with unitary convolution: the [n]-truncation
Jan Snellman
We study a certain truncation of the ring of arithmetical functions with unitary convolution, consisting of functions vanishing on arguments >n. The truncations are artinian monomi…
The ring of arithmetical functions with unitary convolution: General Truncations
Jan Snellman
Let A denote the ring of arithmetical functions with unitary convolution, and let V be a finite subset of the positive integers having the property that for every v in V, all unita…
A poset classifying non-commutative term orders
Jan Snellman
We study a certain poset on the free monoid on a countable alphabet. This poset is determined by the fact that its total extensions are precisely the standard term orders. We also…