同质无等腰空间

IF 1.8 2区数学 Q1 MATHEMATICS

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas Pub Date : 2024-01-01 Epub Date: 2024-05-21 DOI:10.1007/s13398-024-01587-y

Christian Bargetz, Adam Bartoš, Wiesław Kubiś, Franz Luggin

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引用次数: 0

摘要

我们研究了度量空间的同质性问题，在这些空间中，所有不同点的三元组都有成对的不同距离；这种空间被称为无等腰空间。特别是，我们将所有同质无等腰空间描述为二元场上的向量空间，并赋予其注入式规范。利用无等腰分解，我们提供了任意同质有限度量空间中最大距离数的边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Homogeneous isosceles-free spaces.

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Homogeneous isosceles-free spaces.

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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来源期刊

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 数学-数学

CiteScore

4.70

自引率

17.20%

发文量

151

审稿时长

>12 weeks

期刊介绍： The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.