负型有限半度量空间的幅值函数的单调性
On the monotonicity of magnitude functions of negative type finite semimetric spaces
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中文总结 AI 辅助
该研究解决有限半度量空间的幅值函数单调性问题，证明点数≤3的负型半度量空间幅值函数单调递增，同时构造出点数≥4的此类空间，其幅值函数非单调递增。
中文摘要 AI 辅助
受负型度量空间幅值函数的猜想单调性驱动，我们研究有限半度量空间（即“不满足三角不等式的度量空间”）的单调性问题。我们完全解决了该问题：证明了点数至多为3的负型半度量空间的幅值函数满足单调性，同时构造了点数至少为4的负型半度量空间，其幅值函数非单调递增。
英文摘要
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.
