The set of minimal distances of the monoid of plus-minus weighted zero-sum sequences and applications to the characterization problem

TL;DR

This paper studies the minimal distances in monoids of plus-minus weighted zero-sum sequences, advancing understanding of their arithmetic properties and applying findings to the characterization problem in algebraic number theory.

Contribution

It extends previous work by analyzing the set of minimal distances and explores their implications for the characterization problem.

Findings

Identified properties of minimal distances in these monoids

Connected minimal distances to algebraic number theory applications

Provided new insights into the structure of weighted zero-sum sequences

Abstract

Recently a systematic investigation of monoids of sequences of plus-minus weighted zero-sum sequences had been started, which is among others motivated by applications to monoids of norms of algebraic integers. In the current paper these investigations are continued. The focus is on the set of minimal distances of these monoids, which is an important arithmetical invariant. Applications to the characterization problem are discussed as well.