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Homogeneous isosceles-free spaces

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arxiv 2305.03163 v3 pith:XCYQYNP4 submitted 2023-05-04 math.LO math.CO

Christian Bargetz , Adam Bartoš , Wies{l}aw Kubiś , Franz Luggin This is my paper
classification math.LOmath.CO
keywords spacesisosceles-freehomogeneousdistancesmetricadmitarbitraryaspects
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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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