Dimensions of tight spans
Combinatorics
2007-05-23 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/0407317,
title = {Dimensions of tight spans},
author = {Mike Develin},
journal= {arXiv preprint arXiv:math/0407317},
year = {2007}
}
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7 pages