How rigid the finite ultrametric spaces can be?

O. Dovgoshey; E. Petrov; H. -M. Teichert

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arXiv · 1511.08133

How rigid the finite ultrametric spaces can be?

O. Dovgoshey·E. Petrov·H. -M. Teichert

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Abstract

A metric space $X$ is rigid if the isometry group of $X$ is trivial. The finite ultrametric spaces $X$ with $|X| \geq 2$ are not rigid since for every such $X$ there is a self-isometry having exactly $|X|-2$ fixed points. Using the representing trees we characterize the finite ultrametric spaces $X$ for which every self-isometry has at least $|X|-2$ fixed points. Some other extremal properties of such spaces and related graph theoretical characterizations are also obtained.

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O. Dovgoshey, E. Petrov, H. -M. Teichert. 2015-11-25. How rigid the finite ultrametric spaces can be?. https://arxiv.org/abs/1511.08133

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