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Dimensions of tight spans

Mike Develin
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Abstract

Given a finite metric, one can construct its tight span, a geometric object representing the metric. The dimension of a tight span encodes, among other things, the size of the space of explanatory trees for that metric; for instance, if the metric is a tree metric, the dimension of the tight span is one. We show that the dimension of the tight span of a generic metric is between the ceiling of n/3 and the floor of n/2, and that both bounds are tight.

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Mike Develin. 2004-07-18. Dimensions of tight spans. https://arxiv.org/abs/math/0407317

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