4 papers
math.CO2026
On the chromatic number and equilateral dimension of with the tropical norm
Amnon Rosenmann
We study the tropical chromatic number of , , the minimal number of colors needed to color , so that no two points at tr…
math.CO2026
Tropical balls, geodesics and honeycomb
Amnon Rosenmann
In these notes we describe the geometry of tropical balls in equipped with the tropical metric. After defining the tropical length of rectifiable curves (and not jus…
math.MG2026
Tropical measures, anisotropic isoperimetric inequality and honeycomb
Amnon Rosenmann
We introduce a tropical spherical measure on that is based on the tropical metric and is an analogue of spherical Hausdorff measure. This measure is translation inva…
math.RA2025
On matrices in finite free position
Octavio Arizmendi, Franz Lehner, Amnon Rosenmann
We study pairs of square matrices that are in additive (resp. multiplicative) finite free position, that is, the characteristic polynomial (resp. …