Magnitude function determines generic finite metric spaces

Jun O'Hara

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arXiv · 2401.00786

Magnitude function determines generic finite metric spaces

Jun O'Hara

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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.

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Jun O'Hara. 2025-09-03. Magnitude function determines generic finite metric spaces. https://arxiv.org/abs/2401.00786

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