Homogeneous isosceles-free spaces.

IF 1.8 2区 数学 Q1 MATHEMATICS
Christian Bargetz, Adam Bartoš, Wiesław Kubiś, Franz Luggin
{"title":"Homogeneous isosceles-free spaces.","authors":"Christian Bargetz, Adam Bartoš, Wiesław Kubiś, Franz Luggin","doi":"10.1007/s13398-024-01587-y","DOIUrl":null,"url":null,"abstract":"<p><p>We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called <i>isosceles-free</i>. 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.</p>","PeriodicalId":54471,"journal":{"name":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","volume":"118 3","pages":"118"},"PeriodicalIF":1.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11108961/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13398-024-01587-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/21 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

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.

Abstract Image

同质无等腰空间
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。
求助全文
约1分钟内获得全文 求助全文
来源期刊
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信