Dimensions of tight spans
Mike Develin
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 the ceiling of n/3 and the floor of n/2, and that both bounds are tight.
Create a lesson
Related papers
Off-Diagonal Induced Ramsey Numbers
Bruno Andrades, Marcelo Campos, Rafael Filipe et al.
Largest Sperner families with bounded VC-dimension
Gennian Ge, Hanyu Wang, Zixiang Xu et al.
Proof of two conjectures on the log-concavity of partition ranks and cranks
Jianxi Mao, Wenle Shi, Bao-Xuan Zhu
The Exact Number of Pentagons in Book-Free Graphs
Wentao Hu
A family of symmetric counterexamples to the bent sum decomposition conjecture
Máté Róbert Kepes, Anita Kercsó-Molnár, Viczián András
Counting graphs admitting a strictly matched involution
Stephan Dominique Andres, Igor Režan