2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71934Given 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.7 pagesCombinatoricsMetric Geometry51K05; 05C12; 52B45text