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Excess inertia of finite metric spaces
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.
Related
- Isometric copies of ℓ∞n in Lipschitz-free spaces over finite metric spaces
- Continuity of the magnitude for finite metric spaces with nonnegative weightings
- Finite-Sample Bounds for Fréchet Means of Dependent Data in Metric Spaces with Curvature Bounded Above
- A Weak Topology on Metric Spaces
- The Sunada method on Metric Measure Spaces
BibTeX
@misc{gomi2026excess,
title = {{Excess inertia of finite metric spaces}},
author = {Kiyonori Gomi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18132},
eprint = {2610.18132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18132},
}
RIS
TY - UNPB
TI - Excess inertia of finite metric spaces
AU - Kiyonori Gomi
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18132
UR - https://arxiv.org/abs/2610.18132
AB - 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.
ER -