Magnitude function determines generic finite metric spaces
Metric Geometry
2025-09-04 v6
Abstract
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the asymptotic behavior of the magnitude function.
Keywords
Cite
@article{arxiv.2401.00786,
title = {Magnitude function determines generic finite metric spaces},
author = {Jun O'Hara},
journal= {arXiv preprint arXiv:2401.00786},
year = {2025}
}
Comments
19 pages, 4 figures