English

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}
}

Comments

36 pages

R2 v1 2026-06-28T10:26:11.951Z