The betweenness relation distinguishes non-similar pairs of concentric circles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00639753" target="_blank" >RIV/67985840:_____/25:00639753 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00025-025-02514-2" target="_blank" >https://doi.org/10.1007/s00025-025-02514-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-025-02514-2" target="_blank" >10.1007/s00025-025-02514-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The betweenness relation distinguishes non-similar pairs of concentric circles

Popis výsledku v původním jazyce

Two subsets A, B of the plane are betweenness isomorphic if there is a bijection f:A→B such that, for every x,y,z∈A, the point f(z) lies on the line segment connecting f(x) and f(y) if and only if z lies on the line segment connecting x and y. In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when the sets A, B belong to the family Ac of unions of pairs of concentric circles in the plane. We prove that A,B∈Ac are betweenness isomorphic if and only if they are similar. In particular, there are continuum many betweenness isomorphism classes in Ac, and each of these classes consists exactly of all scaled translations of an arbitrary representative of the class. Furthermore, we show that every betweenness isomorphism between sets A,B∈Ac is exactly the restriction of a scaled isometry of the plane.

Název v anglickém jazyce

The betweenness relation distinguishes non-similar pairs of concentric circles

Popis výsledku anglicky

Two subsets A, B of the plane are betweenness isomorphic if there is a bijection f:A→B such that, for every x,y,z∈A, the point f(z) lies on the line segment connecting f(x) and f(y) if and only if z lies on the line segment connecting x and y. In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when the sets A, B belong to the family Ac of unions of pairs of concentric circles in the plane. We prove that A,B∈Ac are betweenness isomorphic if and only if they are similar. In particular, there are continuum many betweenness isomorphism classes in Ac, and each of these classes consists exactly of all scaled translations of an arbitrary representative of the class. Furthermore, we show that every betweenness isomorphism between sets A,B∈Ac is exactly the restriction of a scaled isometry of the plane.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-31529X" target="_blank" >GX20-31529X: Abstraktní konvergenční schémata a jejich složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

1420-9012

Svazek periodika

80

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

196

Kód UT WoS článku

001567833300002

EID výsledku v databázi Scopus

2-s2.0-105015425285