Homogeneous isosceles-free spaces

Christian Bargetz, Franz Luggin, A. Bartoš, Wiesław Kubiś

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.

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Metric spaces, metrizability (54E35) Metric geometry (51F99) Coloring of graphs and hypergraphs (05C15) Models with special properties (saturated, rigid, etc.) (03C50) Group actions on combinatorial structures (05E18)

This page was built for publication: Homogeneous isosceles-free spaces

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6509961)