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arXiv · 2610.18132

Excess inertia of finite metric spaces

Kiyonori Gomi
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Abstract

This paper classifies the possible inertias that are realized by an excess matrix of a finite metric space with at most nine points. For the classification, we make use of relationships between finite metric spaces and non-obtuse and acute sets in classical geometry. As an application, we prove that the small-scale limit of the magnitude function of any six-point metric space is at least one whenever this limit exists.

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BibTeXRIS

Kiyonori Gomi. 2026-10-13. Excess inertia of finite metric spaces. https://arxiv.org/abs/2610.18132

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