Homogeneous isosceles-free spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911887571025920 |
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| author | Bargetz, Christian Bartoš, Adam Kubiś, Wiesław Luggin, Franz |
| author_facet | Bargetz, Christian Bartoš, Adam Kubiś, Wiesław Luggin, Franz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homogeneous isosceles-free spaces Bargetz, Christian Bartoš, Adam Kubiś, Wiesław Luggin, Franz Logic Combinatorics 03C50, 20B25, 51F99, 54E35, 05C15, 05E18 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. |
| title | Homogeneous isosceles-free spaces |
| topic | Logic Combinatorics 03C50, 20B25, 51F99, 54E35, 05C15, 05E18 |
| url | https://arxiv.org/abs/2305.03163 |