Annals of Combinatorics

, Volume 10, Issue 1, pp 53–61 | Cite as

Dimensions of Tight Spans

Original Paper

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
$$ {\left\lceil {\frac{n} {3}} \right\rceil } $$
and
$$ {\left\lfloor {\frac{n} {2}} \right\rfloor } $$
that both bounds are tight.

Keywords.

tight spans finite metrics geometric representation tree metrics 

AMS Subject Classification.

51K05 05C12 52B45 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.American Institute of MathematicsPalo AltoUSA

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