Identification of finite circular metric spaces by magnitude and Riesz energy

2024/08/12 by Kodama, Hiroki, O'Hara, Jun
#51F99 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2408.06091

Abstract

We study the problem whether regular polygons and cycle graphs can be identified by the magnitude or the discrete Riesz energy. We give an affirmative answer for a finite number of cases when the number of vertices is small and a negative answer for an infinite number of wide cases by giving a way to construct non-isometric spaces, which we call isomers, with the same magnitude or the discrete Riesz energy. We study whether isomers can be distinguished by the magnitude homology groups.

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