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arXiv · 2608.15720

On the monotonicity of magnitude functions of negative type finite semimetric spaces

Kiyonori Gomi·Hiroshi Tsuji
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Abstract

Motivated by the conjectured monotonicity of the magnitude functions of metric spaces of negative type, we investigate the monotonicity problem for finite semimetric spaces, namely, ``metric spaces without the triangle inequality''. We completely resolve this problem by proving that the monotonicity holds for negative type semimetric spaces with at most three points, while constructing negative type semimetric spaces with at least four points whose magnitude functions are not monotonically increasing.

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Kiyonori Gomi, Hiroshi Tsuji. 2026-08-16. On the monotonicity of magnitude functions of negative type finite semimetric spaces. https://arxiv.org/abs/2608.15720

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