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Dimensions of Tight Spans
Mike Develin
American Institute of Mathematics, 360 Portage Ave., Palo Alto, CA 94306-2244, USA
develin@post.harvard.edu
Annals of Combinatorics 10 (1) p.53-61 March, 2006
AMS Subject Classification: 51K05, 05C12, 52B45
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 and , and that both bounds are tight.

Keywords: tight spans, finite metrics, geometric representation, tree metrics

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