, Volume 33, Issue 2, pp 199-213,
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Dissimilarity maps on trees and the representation theory of SL m (ℂ)

Abstract

We prove that m-dissimilarity vectors of weighted trees are points on the tropical Grassmannian, as conjecture by Cools in response to a question of Sturmfels and Pachter. We accomplish this by relating m-dissimilarity vectors to the representation theory of SL m (ℂ).

This work was supported by the NSF fellowship DMS-0902710.