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

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.

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