Carl, Uri; O’Neill, Kevin W.; Ryder, Nicholas Establishing a metric in max-plus geometry. (English) Zbl 1398.51007 Undergrad. Math J. 13, No. 2, 159-173 (2012). Summary: Using the characterization of the segments in the max-plus semimodule \(\mathbb{R}_{\max}^n\), provided by V. Nitica and I. Singer in [Optimization 56, No. 1–2, 171–205 (2007; Zbl 1121.52002)], we find a class of metrics on the finite part of \(\mathbb{R}_{\max}^n\). One of them is the Euclidean length of the max-plus segment connecting two points. This metric is not quasi-convex. There is exactly one other metric in our class that does possess this property. Each metric in our class is associated with a weighting function, which is concave and non-decreasing. MSC: 51F99 Metric geometry 15A80 Max-plus and related algebras Citations:Zbl 1121.52002 PDFBibTeX XMLCite \textit{U. Carl} et al., Undergrad. Math J. 13, No. 2, 159--173 (2012; Zbl 1398.51007) Full Text: Link