Annals of Combinatorics

, Volume 10, Issue 1, pp 53–61

Dimensions of Tight Spans

Original Paper

DOI: 10.1007/s00026-006-0273-y

Cite this article as:
Develin, M. Ann. Comb. (2006) 10: 53. doi:10.1007/s00026-006-0273-y


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


tight spansfinite metricsgeometric representationtree metrics

AMS Subject Classification.


Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.American Institute of MathematicsPalo AltoUSA