Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Gomi, Kiyonori
Institution: Institute of Science Tokyo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221792383