Andreas Philipp

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math.NT2011

A precise result on the arithmetic of non-principal orders in algebraic number fields

Andreas Philipp

Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if an…

math.NT2011

A characterization of arithmetical invariants by the monoid of relations II: The monotone catenary degree and applications to semigroup rings

Andreas Philipp

The investigation and classification of non-unique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. G…

math.NT2011

Arithmetic-Progression-Weighted Subsequence Sums

David J. Grynkiewicz, Andreas Philipp, Vadim Ponomarenko

Let $G$ be an abelian group, let $S$ be a sequence of terms $s_{1}, s_{2}, ..., s_{n} \in G$ not all contained in a coset of a proper subgroup of $G$ , and let $W$ be a sequence of $n$ cons…