Homogeneous isosceles-free spaces
Logic
2024-05-28 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.2305.03163,
title = {Homogeneous isosceles-free spaces},
author = {Christian Bargetz and Adam Bartoš and Wiesław Kubiś and Franz Luggin},
journal= {arXiv preprint arXiv:2305.03163},
year = {2024}
}
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36 pages