English

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

R2 v1 2026-06-28T14:06:02.434Z