2004/07/18 by Mike Develin, Develin, Mike
Mathematics · #05C12 #51K05 #52B45 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #math.CO #math.MG #msc:05C12 #msc:51K05 #msc:52B45
paper · pdf · doi:10.48550/arxiv.math/0407317
7 pages
arxiv created 2004/07/18 · openalex publication_date 2004/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the ceiling of n/3 and the floor of n/2, and that both bounds are tight.