Abstract
AbstractWe 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.
Funder
Grantová Agentura České Republiky
Akademie Věd České Republiky
Austrian Science Fund
University of Innsbruck and Medical University of Innsbruck
Publisher
Springer Science and Business Media LLC
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