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arXiv · 2305.03163

Homogeneous isosceles-free spaces

Christian Bargetz·Adam Bartoš·Wiesław Kubiś·Franz Luggin
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Abstract

We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to isometry as vector spaces over the two-element field, endowed with an injective norm. Using isosceles-free decompositions, we provide bounds on the maximal number of distances in arbitrary homogeneous finite metric spaces.

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Christian Bargetz, Adam Bartoš, Wiesław Kubiś, Franz Luggin. 2024-05-27. Homogeneous isosceles-free spaces. https://doi.org/10.1007/s13398-024-01587-y

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